Elon has said multiple times that he won't go public before Mars stuff has happened.

Gwynne Shotwell has said they could spinoff Starlink as its own company and IPO it and use that money to fund more Mars projects if they run out of money. But if Starlink is profitable once it is up and running why would they sell it off/IPO? Just keep taking the money over years probably will work better in the long term.