Regarding why trans people say they have always felt like x or y, what they are trying to express in colloquial and layman’s terms is the concept of gender identity, now more commonly referred to as either social sex identity and physical sex identity, which it two concepts, each distinct.
Roughly translated, the whole thing means that a Trans person is aware that they are a woman, man, both, or neither, at the same core level as they are aware of themselves as a person, distinct from other people.
Some people would prefer to argue that what this is suggesting is that there is a “brain sex” — and yet, that’s not what this is describing. It is describing a sense of self-awareness — which, while decidedly part of the brain’s physiology, is really part of the existential notion that one exists, and therefore is not part of that argument, nor even related directly to biological systems (though many studies indicate such, I’m not going to reference such as biological essentialism of that sort is somewhat contrary to existential systems such as Transcentrism).
What that means, as well, is that this description has nothing whatsoever to do with biology, and, therefore arguments about biology aren’t valid when contradicting it. It would be akin to saying that the United States army shouldn’t exist because of broccoli.
This all comes together in the core aspect here: like sexual orientation, this is part of what creates the sense of self in people, and it therefore is part of how they know that they exist as an individual human being, and is a part of that.
So the same question of how you know can be answered in as many different ways as there are people, and it is the still same way that those asking the question know what their social sex identity is.
This effectively makes it the trans version of the question “how do you know you are gay?”, with the same accurate answer “I just do, because I know I exist.”
The answer may not satisfy those seeking some sort of concrete answer, but it is inevitable that they themselves, will discount any answer because for them the same question remains unanswered in a way they would accept from a trans person, usually due to cis privilege.