Can I play Star Crossed if I have no cards to send back to my hand?

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

As established by RiftJudge FAQ #9865, #10187, and #10769, Star-Crossed specifically requires both a friendly unit and an enemy unit to be present on the board 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. If you do not have a friendly unit to target, you cannot fulfill the requirements of the spell, and therefore you cannot play it.