You don't have to "know" you have a problem to cope with it, that's one of the interesting ways the human psyche works.
I didn't "know" I was trans, I was in denial.
The denial was a coping mechanism, a way to avoid knowing, a way to ignore it, a way to carry on.
As a part of denial, I did a lot of things. These things were also coping, and yet, I didn't "know". I had no "awareness".
I didn't even "know" as a child.
I knew something wasn't right, and I was angry about my puberty, and I had a lot of self loathing, but the why wasn't there, I didn't know that why, and during and after puberty I even took the whole "something wasn't right" and shoved that further down, into denial.
I didn't want to be a man, when I was 15.
I didn't think of myself as a man, when I was 15.
Because I was in denial.
I didn't even register that trans men existed, even if I had the chance to know more than once, because I was in denial.
Our minds are powerful things. If we're in the right frame of mind at the right time we can cause our very flesh to change. We can give ourselves bruises and burns really just from thought.
It's not unreasonable to think it easily possibly for the mind to be able to create a situation where we do not have any knowledge or understanding of us being trans, even for a number of years.
And to top it off, our memories are malleable. They aren't like pages in a book, they're changeable. Enough denial and we might wake up one day sure that we've never, ever, not even once felt "trans" before, because there's nothing in our memories that suggests we ever did, because we've changed our memories to fit the denial. It's also possible for the memories to change (again) once we've figured ourselves out. We can realize that we're trans, and suddenly remember all kinds of things about feeling this way our whole lives, even if we actually didn't, not as such.
This means that it isn't all that obvious and that the mind can easily make it impossible to realize at the time. If not only because we can't face being "one of those".
And yes. A man can be in denial over a missing leg. He can actually see the whole leg, just "non-functional". The mind can fill in all kinds of reasons why the leg doesn't support his weight. It's part of why the brain's such an incredibly fascinating organ.