Your best bet (IMO) to get the vaccine earlier is to look for info from a vaccination site/provider that indicates they have doses unaccounted for (nobody to take them) and they're willing to vaccinate without regard to eligibility. This has been happening some. Watch the news, get on notification lists, network with friends, coworkers, relatives.
Myself, I'm eligible by my state's standards and those of my healthcare provider, but I know people who've had their shot(s) who I think are not. I don't know how they got theirs.
Meantime, mask up well (get KN95's if you can, double mask), socially distance, take your vitamin D, vitamin C too, get your rest, eat well, don't take chances! Good luck!