Are there any professional sports leagues (CFL, NHL, ...) where it is possible to call a timeout before the game actually starts? Has this ever actually happened?
Yes. Time-outs may be called (FIVB Rulebook 2021-2024, 15.4.1)
when the ball is out of play and before the whistle for service.
with no further restrictions. Hence they can be called in the window between when the teams have entered the court before the first point and when the first referee blows the whistle for the first serve.
Has this ever been done professionally? Don't know - but we did do it once in one of my club matches; our coach was delayed in traffic and arrived late at the venue. We then took both the timeouts we were entitled to for the first set before the first service so our coach could say what he wanted to say.