If you read Daphne du Mauriers letters it's very clear that she didn't feel 'normal'. It caused her a lot of anguish over most of her life - probably a lot of women did. I guess it's hard for us to fathom, but when you're literally constrained with what you can do, where you can go, who you can speak to, because of (what are now considered) arbitrary social rules, then yes of course, you'll feel unhappy and anguished about it. Even more so if religion drives some of it.
What exactly do you mean when you say 'Trans people have always existed'?
Do I believe that people who are unhappy with the social expectations of their sex have always existed? Yes.
Do I believe that people who have tried to subvert these expectations have always existed? Yes.
Do I believe that people who believe they are the actual opposite sex have always existed? Yes - but I also believe that depending on which area of the world you would have been in, you might have been institutionalised because of this belief; you might have been put to death or jailed. Or, your culture might have created a third "space" for you and people like you.
Do I believe that due to the overwhelming patriarchal rule over most of the world for most of human's being on this earth, that women who disguised themselves as men or who behaved as men did it because they believed they were men? No, I believe they knew they were women and were trying valiantly to prove themselves or protect themselves in a man's world.
Do I believe there has always been people who wish they were the opposite sex? Yes. I actually think they were probably a lot more switched on as the obfuscation and terrible medical care of today's world has fumbled this. At least back then, you might feel like you wish you were the other sex but would know that other than cosmetically it would never happen.
Do I believe that trans people exist? Yes, I'm not blind. But sorry, I cannot square the circle that says it's both not a mental health issue but is a physical one that can be fixed by changing how a body looks. Because no matter what small children are growing up to believe, it is not possible to change sex.