I wouldn't be comfortable with 2" of concrete. As Tom said, 3" is a better starting point.
No one says the floor has to extend from wall to wall. But digging a couple of inches deeper shouldn't compromise the building integrity. I'd dig a couple of test pits to see what the actual conditions were. Dig next to the walls; not under them! If there is a footing, it should be wider than the wall ( "should" be).
In some of the older sections of Baltimore, I've seen some basements with 5 feet ( or less) of headroom--since the guy was seated at a workbench when he was down there-he had enough room.
I also prefer a drainage layer (gravel, or sand), but if your conditions are historically dry, and its for your temporary use, you might get by OK.

Get, and WEAR a bump cap--not as strong, or heavy, as a OSHA hard hat, but it will offer some protection from banging your head.

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1982 300SD " Wotan" ..On the road as of Jan 8, 2007 with Historic Tags