How far can a foot soldier reasonably travel in a day if he's alone, in enemy territory, and traveling light? I know this sounds terribly cliche (and even a little moronic) but it's not quite as bad as it sounds. Probably.
Honestly, don’t worry about a concept being cliche! Deep down, nothing is original, right? Just do it in your own way!
Assuming the character isn’t hurt, is in good shape, is traveling light, (say twenty pounds or less of gear, which isn’t much as your boots and weapon are at least eleven pounds on their own, assuming it’s an M16) has had food and water, knows how to handle the terrain, isn’t in extreme conditions, and has cover? Probably up to ten miles.
We’re expected to be able to march 10km (about six miles) in full gear, rain or shine, so I’d say most soldiers should be able to do that much in a day in ideal conditions and light gear, although I’d say each consecutive day they’d be doing progressively worse as they get tired and sore. Walking that much is exhausting for even the hardest soldier.
But every little thing can affect that. Are you in a desert? Too hot. Better travel at night. But you can’t see where you’re going, so you’d still be lucky to do four miles. Is it snowy? Snow is hard to walk on, especially when you’re leaving a trail in the snow in enemy territory. Have they eaten or drank? They’ll be slower if not. Is the terrain familiar, i.e. do they know how to navigate a jungle, desert, etc? Are they in good physical condition or a bit out of shape? Are they infantry or a pencil pusher? Whether they can camouflage themselves matters too, especially if there’s not much cover, because then they have to be more cautious about movement. How alert is the enemy - are they actively searching for you or are you just on their terf?
I guess carefully consider each obstacle in your soldier’s way and be fair. That’s the most important thing about writing: you don’t have to be mean or nice, just be fair.
And remember they need to rest, sleep, and eat. We’re specifically taught that in survival situations we need to sleep and eat, because running yourself ragged in enemy territory is bad and exactly when you can’t afford to pass out. We’re all supposed to know how to boil water properly and how to tell whether the local flora and fauna is edible. That includes bugs.
Btw. We are also taught that if it came down to dying in the wilderness or being captured by the enemy, after making a good faith effort to get to safety, we should choose capture, after disposing of anything valuable or containing intelligence. We do the same if we know capture is imminent. We keep our dog tags. It doesn’t sound noble, but soldiers cost the army a million bucks a pop to make, and if you die that’s another $400,000 paid out to your family and now they have to find someone to replace you. The Army would much rather keep you alive as a POW. But ultimately whether the soldier chooses to be captured is up to them.