According to the Rules, the president may appoint a judge to the supreme court as an interim replacement if the Senate is in recess at the time and the appointment will be good, I believe until the next Senate convenes.
If I were the president, facing a hostile Senate and with an agenda to push, I'd have a nominee on speed dial at all times in case just the situation as just happened arises. Right now the Senate is in recess until Feb 22 so a recess appointment is legit. The ideal candidate would be a disabled female of color or a member of a privileged subgroup who can be counted on to back the presidents agenda. There would be no other qualifications absolutely required although a passing familiarity with the legal system would be a plus.
Complaints about packing the court with malleable crony's would be duly ignored by the MSM. Complainants would be denounced as racist, sexist, or whatever kind of -phobic might apply.
The proper action for Sen McConnell would be to immediately return to the Senate, Gavel it into session, then gavel it into one of those temporary breaks that allow every one to go home without actually declaring a recess.