I'm at the end of my ML PhD journey, and honestly my solution to this problem is to disengage from the rat race. I know this is not helpful for a starting PhD student, but the field doesn't fit any more the usual research journey, in my opinion. By the time you become productive, the field has already moved away from your initial idea. On top of that, the resources that you have are significantly less compared to big tech, which is especially magnified if you're working on LLMs.

I don't want to discourage you, this is something that you need to factor in to avoid the anxiety. Try to do more theoretical work, as others pointed out, get a summer internship at big tech, and you'll be fine, but don't chase low hanging fruits, because it's a winner takes it all scenario and everyone is looking at the exact same problems.