You'll be surprised how much starting T can change your perspective on things like this. When you take T, the way you perceive yourself changes. Right now you may be softer and more timid, but it's not unusual for T to make us more assertive and more confident. You might find that your mind & personality adjust along with your body (as is the case for many of us) and you'll wind up being a more contented, more rounded human being as a result. And it takes many months (or even years) for T to have its full effect, so if you find you don't like it you can always come off it before much has changed.
You'd also be surprised how men get treated in society: it may not be what you think it is. Of course, this all depends on where you live and what the prevailing culture is like, but in my experience both men and women are treated aggressively but the aggression just takes a different form. With men, the aggression is mainly competitive (basically a peeing contest) and sometimes - rarely - it breaks into physical aggression. In my culture, it's mostly in the form of jokes & banter - so getting good at that can be very helpful because it can deflect the other forms of aggression. It's up to you whether you engage with any of that. And of course, women can be aggressive towards men too - but as they're generally physically weaker, it takes different forms - mostly mental, emotional and (where appropriate) sexual. But despite this 'weaker sex' reputation, there are plenty women who have physically attacked both other women... and men.
With women, the aggression they suffer tends to be less physical (generally), but it's more intellectual, emotional, financial and social. In general, women are talked down to by everyone but especially men and they're treated like they can't do anything for themselves. This is sold to us as 'chivalry' and we're told it's a good thing but really, it's a way of infantilising women. It gets very stale very quickly, as most of us who've moved through the world in a female form at one time or another can attest. Then there's things like the glass ceiling, unequal pay for equal work, and a societal assumption that women should be homemakers and primary carers of children and men should be protectors and providers. All of these things really do still exist, and they're all forms of aggression. We just accept them because we've always been told that this is just the way things are done.
If men try to dominate each other, women - of course - do the same thing but with subtle differences. I learned very early on that there's no such thing as a 'sisterhood' of women sticking together to achieve their common goals. Instead, women generally compare themselves to each other, compete against each other for the best man, the best house, the best kids etc. etc. and some of them tend to put each other down so that they can elevate their own social standing. So they also have their own 'peeing contests' but they just take a different form. Which is kinda apt, really.
So there isn't a gender role that is 'perfect' or 'better' than the other. But we tend to find that a particular gender role (or our interpretation of it) is more suitable for us as individuals than another. So when's the perfect time to move over to the right team? The answer is: there's never a perfect time: there never has been, and there never will be. There's only the right time for you - and if that's now, that's now. If it's 5 or 10 or 20 years from now, well so be it.
But know this: dysphoria gets worse as time goes on, and the sooner you start your transition the better your results will be. So if you need to transition, you might as well get on with it - because society never can and never will be perfect for each individual's needs.
There's nothing wrong with being a soft guy. We all have to find our own paths in life, and if that's your path then that's perfectly OK.