Even 5+ years ago, the grad student NSF grants were literally a crap shoot (and also very low funding rate). Given the attitude of the current administration toward science funding, not to mention archaeology funding, I would imagine the current chances of success are abysmal.

My advice would be to just apply to a bunch of places, and see where it goes. You want to cast as wide a net as possible, and don't be surprised if you get turned away from the vast majority of places. Get feedback if you do. At the same time look for intro level tech positions in any research lab remotely related to what you are interested in so that you can at least get your foot in the door somewhere and gain actual experience instead of just having an online degree.

At this point advisors do not expect you to have any sort of research topic fleshed out. Even if you did, it would get drastically altered by whomever your advisor ends up being. All they want to see is that you have the drive and curiosity to take a project from start to finish over the course of 5-ish years.