How do I build a vinyl collection without support from my parents? ?

Are you a child? If not then why does it matter what your parents do? If you’re a child then wait till you’re of legal age to move out and do what you want

Yeah, vinyl records are the best type of record - far better sound quality and far less  fragile than shellac.

I disagree about this being a good time to start collecting records though - that would have been years ago when, apart from collectable rarities, you couldn't even give them away.

If your parents aren't willing to help you collect records (and I don't blame them) then you obviously have to finance it yourself and find somewhere to keep your collection. This might be a problem as, I presume, it's their house and they'll not want a lot of space taken up with something they don't approve of anyway.

You don't say why they disapprove of your collecting “vintage-esque things” or what has happened previously regarding this so it's impossible to suggest how to could get them “on-side”.

How old are you?  Do you have a job?  I can't imagine why they would be against vinyl unless they are paying for it or it takes too much room.

How? Get a job and spend a portion of your pay on vinyl and the associated turntables and amps.

Unless you need financial support from your parents, that question makes no sense.