Can you play Starcrossed when I don't have a unit?

No. You cannot play Star-Crossed unless you control a friendly unit on the board.

The spell reads "Return a friendly unit and an enemy unit to their owners' hands." Both are mandatory targets — there is no "up to" language. At the time you announce the spell and place it on the chain, you must have a friendly unit to target. If you don't control any unit, the targeting requirement can't be met and the spell can't be played.