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Seems like central here is what it means to be trans.  What is the transition process?  When does it begin?  Is it social transition?  HRT?  Exploring gender non-conformity?  What counts and what doesnt?  It's a tough question to answer because I don't think the term is well-defined.  
But someone might, say, engage in some gender non-conformity, realize something about it feels fulfilling or authentic, and gradually feel into that sense of authenticity or beauty only to realize they're some degree or another of trans.  Basically, fuck around and find out.   
I also know some nonbinary people who started down that path only to realize that HRT disagreed with them in some way or another, so they desisted and expressed their queerness in less medical ways.
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Stripped to the studs you seem to be saying that being trans means running away from your old gender, and that— in terms of identity signifier— running to the new gender can be seen as incidental: a byproduct of running from the birth gender.  
The seems odd to me.  Whether someone's transitioning because they're running from something that feels wrong or towards something that feels more correct seems like it shouldn't much matter.    
It seems to me that you're not taking people seriously.  You dismiss people who say they experience euphoria and not dysphoria, claiming they're just lying to themselves, or repressed.  That might be true, but doesn't it seem more likely to you that people simply have a different internal emotional experience than you?  How often do you see people online dismissing the experience of others because they find it illegible based on their experience: {"Why don't you just choose to stop being depressed?"}.  How often do cis people tell you that your trans identity isn't real because they had a phase as a tomboy.  It's good practice to take people at their word {within reason}, and to understand that people's experiences can vary quite a lot from our own.    
RE: knowing euphoria without dysphoria.  This again, seems odd to me.  Surely, you'd know what loving touch felt like even if you'd never been beat. You can find yourself suddenly happy without having first been miserable.  You can discover a new flavor you like more than anything without suddenly realizing that all your gustatory experiences before that were rank torture.  I have a hard time addressing this point because I find the notion fairly confusing, but it feels important to address it, because this seems to be near the heart of things for you.      

It is also medically proven that those who are transgender and experience dysphoria have brain waves that align with the gender they identify as rather than their gender at birth.

Also, just as a point of interest, this actually isn't true in any meaningful way.  Source: phd in neuroscience and keenly interested in that kind of thing.  The science behind such studies is very shoddy, or have lots of qualifiers that mean it doesn't say what people think it does. >

(To your last point) Really? I never knew that. When I did research on it, it was backed up by various studies and proclaimed to be true by experts in that field.
And yes, I do admit in my post that it could be due to my lack of outside experience. Because I experience dysphoria, I cannot understand someone who doesn't. I could very well be trying to rationalize it in a way that makes sense to me and I recognize that, which is why I am here.
I guess the core point no one has explained to me is this: why would someone begin the transition process, should they not experience dysphoria? Does it just seem appealing? I truly do not understand it, and I am trying my best to.