I would look into a month long car rental with someone like enterprise ASAP if you need a vehicle. Not 100 % sure but I think you're going to have some hurdles here. You may have to take a driver's course ... you'll need documentation to prove residency which you may need a month to collect etc.

Not sure but you could ask Dealer if a lease option could be faster but I doubt it.

Either way call the DMV to make sure you're clear on rules to get your license and sign up for that course asap if you need it because it could take time to find one.