I don't know what things look like in your neck of the woods but around here, there are a lot more anglers out on the streams this year (2020). Inland Trout Stamp sales in Wisconsin are up about 22% (for more COVID-related license and stamp sales and what it might mean for the future, read COVID, Fishing, and the Future) and it is pretty noticeable. If you are like me, you enjoy fishing for the solitude and to get away from people. Ok, I'm a bit less concerned about getting away from people in 2020. Although, I generally have a little laugh at people that talk about how crowded Wisconsin streams are (try fishing Pennsylvania's better known streams some time...), our streams can certainly be more crowded than we'd like.
I fish public access points most of the time and quite often in the Coon Creek (Timber Coulee) watershed mostly because it is nearby. It is on the list of top 100 trout streams. It is one of the "sacrificial lambs" - a stream you don't mind naming because EVERYONE knows it. While the watershed is certainly not off the beaten path, there are ways to find water that is less likely to have anglers on it.
Quite simply, the easiest way to get away from others is to fish times and places that they are not willing to fish. Fish small streams. Or really big ones. Get up early. Or fish until late. Fish where roll casting is not optional. Be willing to walk - or paddle. Be willing to do what others are not. Fish during the middle of the week and not weekends - though that is often easier said than done and lately, it is no guarantee of solitude.
Here is a quite incomplete list of ideas for how to find less crowded waters - and often less educated fishes.
Fish small streams and really big ones. Most anglers are fishing in the Goldilocks zone - where streams are neither too small so they're difficult to hit with fly or so large that they're tough to wade and often have low density trout populations.
So the stream above is a *bit* difficult to fish this time of year but in the earlier part of the season, it is quite fishable. Interestingly, the water temp was cooler in August than it was in May when I had last fished this same reach. It provides a nice thermal refuge for trout and helps cool down its receiving waters.
You are probably looking for something a bit more fishable than the image above but fishing smaller streams will often put you in places others are unlikely to fish. There are many options that are fishable throughout the year and some others that fish well through at least May. On the other end of the spectrum, fishing larger "marginal" or transitional areas (cool bass streams / warm trout streams) may get you away from most other anglers. These streams often have lower density trout populations but much larger average sized fish. The are, however, places you'll want to check on temperatures before fishing by mid-June or so.
Fish early and fish late. There is an old adage that trout bite best when the weather is most comfortable for the angler. During the early season, on nice days, the fishing is often the best after the air has warmed up but before the snowmelt hits the stream. In the summer, getting up early and fishing until it starts getting uncomfortably warm and fishing near and after the sun sets can be an effective - and comfortable - strategy.
I do not do it often but a few times a year, getting out "mousing" can be a blast and even on the most popular streams, it is likely to provide some solitude. Or throw some bigger streamers at night and see what happens. Chill out during the middle of the day, find some shade, get a little siesta and fish when others can't or won't.
Fish the better known watersheds and lesser known streams. Ok, this is probably a little confusing but hear me out. I fish the Coon Creek watershed a lot mostly because it is close but also because there are 136 miles of classified trout streams (link). I am all but guaranteed to find at least a mile or so of decent water to fish. The 3 or 4 spots I thought I might fish might be taken but without too much windshield time, I'll find a place to fish.
Some lesser known streams might not provide world class fishing but they may provide the solitude you are looking for. In the vicinity of some of the best known trout streams are other streams that are not as well known, may have lower trout densities, and maybe are a little more difficult to fish but they can be good at times and if you're looking to see fewer people, they may be a good bet. Even within the better known watersheds, there are often streams that relatively few people fish.
Fish before, after, or during the rain. I learned this one early in my trout fishing life. I was probably in my second year of fly fishing and I was enjoying very little success and really no consistent success. As the storm starts rolling in, I could not keep them off my pheasant tail nymph. In fact, the fly was falling apart and they were still hitting it nearly every cast. I had caught at least 30 fish, all on the same battered fly, before the rain became too much and I headed for home, quite pleased with myself having never experienced anything like that before. I assume it is barometric pressure but somehow the trout just know and very often put on the feedbag before a rain. Is it that the bugs are more active? It is more overcast and they feel more secure? Is it an evolutionary response - eat heartily before a rain as it might be lean times for a while? I don't know but the half hour or so before a storm can be spectacular.
At times I've had good fishing during a rainfall but it is much less consistent than before a rain event. What seems to be the best conditions are a drizzle. The worst conditions, in my experiences, are when a large quick moving cold front is pushing in. Some of the best blue-wing olive (BWOs) mayfly hatches are during light rain. I've rarely had good fishing during heavy rain but then again, I do not fish during heavy rain all that often and am quite conservative about cutting it short when fishing a graphite rod and lightening is possible.
Lastly, a topic that deserves a lot more attention is how to fish after a rainfall / flood. This is unfortunately something many of us have learned a lot about in recent years. My experiences, in general, are that fishing as the the stream first starts coming up can be quite good. As the stream moves closer to its peak, fishing tends to decline and continues to be poor for a period of time dependent upon how much the stream came up and how dirty the water got. As the sediment starts to fall out of suspension and the stream clears up, the fishing tends to improve. The falling limb of the hydrograph often keeps the stream a little off color for some period of time. Slightly off color streams can be fantastic because the conditions help but a few things in the angler's favor. Fish tend to be less skittish in turbid waters and with the receding water, fish may not have eaten during the heaviest of the flooding so they are particularly hungry.
Fish "roll-casty" waters. Fish the stuff that most others do not want to. This mostly means fishing more wooded reaches. Yeah, it can be a pain; if you are doing it right, you are going to lose some flies; and it can be more than a little frustrating. However, fishing these difficult places can give you some solitude, put you in places where trout see fewer flies, and provide a challenge.
As mentioned, I fish Coon Creek / Timber Coulee a lot because it is close and there are a lot of options. As you drive along Highway P through the open pastures, often the access points are quite often crowded. It is relatively easy to get around, there is little to catch your backcast, and it can get crowded. Those places are great but if they are more crowded than you would like, go elsewhere. Elsewhere is often going to be places that will test your roll cast and your creativity in getting a fly into tough places. I enjoy this as it is often rewarding to catch fish in places others won't even try to fish. Other days it is frustrating as Hell...
Get away from access points. Quite simply, be willing to cover some ground and do some walking. I don't know the exact statistic but somewhere north of ninety percent of all people that go to Yellowstone National Park never travel more than a mile from a road. A similar thing often happens on trout streams. A huge percentage of angling pressure is concentrated around bridges and other access points. Get away from them and you are likely to see few people and encounter fish that have seen fewer people.
If you are fishing by yourself, it means being willing to do some walking. With a partner, leave a car at one access and fish to it from another access. On some larger streams, a canoe or kayak can provide access to difficult to reach waters that see few anglers. It is not something you can do every day but it might be a good way to get away from people. I've had days where I have asked other anglers how far up or down they are planning on going, given the stream a wide berth, and started fishing further from an access point knowing I was going to fish to the next access point.
Fish private property (legally). Wisconsin's public trust doctrine states that all navigable waters are "common highways and forever free" and the waters of the state are public resources. The public trust doctrine defines navigable as any waterway on which it is possible to float a canoe or small watercraft at some time during the year. This means that compared to many other states - I'm looking at you, Colorado - Wisconsin has pretty liberal public access laws. Stream access laws in Wisconsin (link) allow you to "keep your feet wet" and enter private property to go around wading obstacles, including deep water. However you must not fish while doing so and must re-enter the stream as quickly as safely feasible. You can enter through road right of ways which are typically (but not always) 33 feet on either side of the road centerline or about 23 feet from the edge of the road (link) or any public access point. Of course, it is your responsibility to know the laws of your state and not all roads have the same right of way.
This all sets up the fact that streams in Wisconsin are owned by all of us and you have legal access to any navigable stream that you can legally access. It means that almost every trout stream in Wisconsin is public.
To be honest, legally accessing streams flowing through private property is not my favorite way to fish but I will do it. Landowners don't always know the access laws and will sometimes illegally harass you (link to Wisconsin interference with hunting, fishing, and trapping legislation). Sometimes they simply do not like you being there whether or not they understand that it is legal. It is always better to ask permission but it is not always possible, particularly in rural areas. Legally fishing streams that flow through private lands will 1) get you away from people, and 2) likely give you access to fish that have not seen a lot of anglers.
Just be sure to know the laws and follow them as failure to do so can earn you a fine and give anglers a bad name. I've known an angler or two that carry paper copies of the rules or have them downloaded to their phones in case they run into hostile landowners. Planning for confrontation is not something that much interests me so I tend to fish easements and public lands. But there are good reasons to fish streams flowing through private lands. Just do so with respect and within the law.
In summary, anything you do that others are not willing or able to do increases the odds that you are going to have some solitude. If you're willing to expend a little more time and energy than others, willing to get a little wet, and willing to lose a few flies, you are more likely to "have the place all to yourself".