It's not uncommon to feel the way you are during the second and third years - my advice is to recognise how you're feeling and then work out how to push forward (which is what you've already started to do).
My advice for how you can compete with large research projects full of postdocs is, don't try to. You're not in competition with them, you are doing your own research. It might be in a tiny niche area, but it's your area and it's new knowledge.
ignore the prestige games, knuckle down and do the best work you can do- it’s more impressive if you succeed at a lower rank institution anyways, imo. And if you want that signalling power you can always plan to go for a postdoc.
Wishing you the best of luck, it can be a lonely path.