The Judiciary Act of 1869 fixed the number of Justices at nine and no subsequent change to the number of Justices has occurred.
Appointment must be with the advice and consent of the Senate. To me, that means it must be the Senate that is in place when the appointment is made, which can’t be made until there is a vacancy to appoint to. I don’t think the President can bank a confirmation in advance of a new Senate. But of course, the 6-3 Supreme Court finds in the Constitution whatever suits it.
I just dumped an almost-completed post about the legal procedural obstacles because it was unclear to me where that issue fell between the narrowest reading of the OP’s question (“Is this idea legal under settled proven law?”) versus the OP’s request and moderator reinforcement to not get bogged down in what I at least perceive to be questions of the political viability of the idea.
“No change has occurred” is not equivalent to “No change can occur”.