You will need some parking permit at Marble Mountain Sno-Park. I am never sure this time of year which one you need, so I'd recommend calling the GPNF station. If nothing else, it they are wrong you could dispute a ticket given you got bum info from the forest service. The same would not be true for bum info from some schmoe like me on CC.com.
There are 2 lots there, one for overnight parking.
On May 13th, tons of people boot packed it up. No need to any flotation.
Best of luck on your climb.
-r