If you can get to a land crossing, you can cross in a "private vehicle" with the proper paperwork (or you used to be able to. I'd check with an attorney as well.) When I did it ~5 years ago, I had my entire application copies, my original landing paper. (IMwhateveritis - the long brown and white thing) and anything else I felt might help establish my residency. They glanced at my paperwork for 2 seconds and I rolled through. The times being what they are I should note I'm a yt male and was in a rental car - did a Buffalo to Pearson drop off - but rental car compaies aren't doing that anymore cuz Covid. You could get someone to come get you, or probably do an uber/lyft kind of thing. Or go round trip to get your card and bring the car back. It's a pain, but it can be done
I had checked in with an attorney before I left Canada to be sure it was cool, they assured me it was. I am going to check with them again to see if anything has changed. Basically, unless they want to try to pull your Resident status (which is a process that take some time) they had to let you in (they had to let you in even if they wanted to pull it, and you could appeal/fight it, but it might affect getting your card, I guess.) So, basically if you can get in the states with no hassle, and your application is otherwise legit, you used to be able to cross in private vehicle. I assume, but have not verified, this is still correct.
Hope this helps.