Locally I’ve seen 1 early 20-something sky rocket past 300W in the first six months or so. And from talking to my 25 year old buddy, most of them took several years to develop to that point.
Did they weigh 85kg or near?
22y, probably good body composition, maybe little life responsibilities, healthy and has time to train.
Of course nobody can guarantee things, but why not?
With 22y I slept until 11, went few hours to university, ate a shitload of carbs and trained daily like a berserk (not cycling). These has zero to do with the jelous old people here trying to stay alive between job, family mortage and health issues (me included) trying to talk you out of trying yourself.
Train a lot, lay out some reasonable progression, eat and absolutely figure out and maintain good form. Getting hurt = no training = no gains. Your youth will figure the rest out.
It’ll be hard but you’ve got youth on your side and with work its possible 
It’s definitely a “soft” goal for me, if I don’t hit it, then oh well, if I do then it’s worth a little bit more.
I’ve been through a rehab journey once before, not planning on doing it again, can only bail yourself out with youth so many times 
Figners crossed.
As others have said, it’s really hard to know until you get into it. If you were totally untrained aerobically and your first ramp test was ~180w, that would indicate a lot of potential. But you said you are riding 6-8 hours a week. Even if that has zero structure and you are just going easy, that’s very different from someone who is totally untrained. New riders can see a bunch of improvement in the first 6-12 months with consistent training, but every additional watt is harder to get as you work toward your genetic potential (takes multiple years, not months to get close). If your genetic potential is to have a 450 watt FTP, it would be more realistic to get to 300 in a pretty short period. If your genetic potential is only 350, it’s very unlikely you’ll be seeing 300 in a short period of time. The initial gains are easy, but the curve gets flat in a hurry and there is no way to rush it (at some point, more training will hurt rather than help).
Some people have high potential, but are slow to adapt. Others respond to training quickly but may not have the same genetic ceiling. We’re all different. Setting a 300w FTP goal is fine if that floats your boat, but I’d suggest getting at least 6 months of training in before even speculating what a reasonable FTP goal looks like. In the meantime, you might consider a “process” goal that you can control such as consistently doing structured training sessions at least x times per week.
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I think you could do that and maybe even more