We just did that this summer!
We drove all night to WDW, and checked into the Grand Floridian at 6:00 AM! They were actually able to get us a room - if not, we were prepared to change in the locker rooms by the pool.
You don’t even have to check in if you don’t want to - just tell them that you’ll be checking in that day.
We’ve also gone straight to the parks before and just told the CM at parking that we were checking into our resort that day, and they’ll waive your parking fee.
Whatever way you decide to do it, you won’t have to pay for parking!