I've done this before and my best advice is to FIRST give the paint plenty of time to completely dry and harden.
There's dry to the touch and dry to the bone.... you want that paint dry to the bone as in the entire thickness or matrix of paint to be completely dry.
Unless there's a hurry, I would wait a few weeks and if possible, park the car in the sun during the day so the paint heats up.
Besides that, if you have a DA Polisher get everything you need to dampsand the paint. If you want to be careful start with the #1500 Foam backed finishing discs. If you are confident there's lots of paint then start with the #1500 Sanding discs, no foam backing on the disc.
I would still use an interface pad because it helps the sanding disc to flex over body panel curves, otherwise you're sanding with a 100% flat surface, that is hard flat surface on the backing plate and thin piece of sanding disc.
After you cut it with #1500, (either one), then re-sand using the #3000 Foam Backed Finishing Discs.
Then cut with a good compound and a wool pad, then switch to a foam pad and re-buff each square inch, and then finish out with a DA Polisher.
I cover the entire process here,
Damp-Sanding Tools, Tips and Techniques by Mike Phillips
That paint is soft even after it's completely dry and set-up so buffing out sanding marks will be a breeze...
You can also hand sand it which is cheaper but more labor intense and time consuming. Matt and I dampsanded a 1956 Chevy from start to finish in about an hour.
Dampsanded
After Buffing
Try to work in a garage out of the sun... black paint gets hot and the heat will make the paint softer than if it were in the shade...
Take good before pictures as you can never go back in time and get them after you've sanded and buffed the paint...
The power in the after shots is created in the before shots
Be sure you have a spur for your wool pad... you're going to need it...
