I don’t think there is any Supreme Court case that says it, but when Clinton was President, that was the argument that was made about what had to take place. Impeachment first, then prosecution. I suspect the Supreme Court would agree.
The only wild card I see here is that the criminal act occurred before she would have become President. Maybe that makes a difference.
Why would the supreme court agree? Where does the constitution or federal law give the executive branch immunity from prosecution?