Ahh, Ohio!
I went to Dave's Garden calendar under "Goodies" and typed in "Ohio"...
It suggested direct-sowing pumpkins between May 19 and Jun 18.
http://garden.org/apps/calenda...
No transplanting out?!? I guess not.
I don't think I've ever seen pumpkin "starts" for sale, so that probably isn't an option to speed things up.
A few years back, I started cruising seed catalogs and websites for when-to-plant advice, and made up some "calendars".
I figured that I would use those for my first guesses, record results, adjust, and try again. I thought it would only take a few years of trial-and-error to get my dates as accurate as naturally-varying weather permits.
Instead, work got busy and I barely have time to weed the beds, let alone plant.
That might be good because in the meanwhile, someone moved in who does a lot of gardening. After I retire, I going to introduce myself and have a long talk with him. Picking his brains should give me a local leg up.