Can I Star Crossed with no units?

No, you cannot play Star-Crossed if you have no friendly units on the board.

According to RiftJudge FAQ #9865, #10187, and #9452, Star-Crossed requires both a friendly unit and an enemy unit to be present as valid targets to be played. Because the spell lacks "up to" language, both are mandatory targets. You must control a friendly unit on the board to serve as a valid target for the spell at the time it is announced and placed on the chain.