A president can pick whenever he wants, the question is does the Senate have a duty to confirm or even consider that choice. I think history has shown that the answer to that depends upon who's controlling the Senate at the time, and they obviously can have it both ways since they're under no constitutional mandate.
What's telling is that virtually everyone changes their mind on what should be done based upon who's doing it. It's not just Republicans who believed one way in 2016 and now possibly think differently in 2020, it's also the Democrats. How can you assign hypocrisy to just one team?