None of the following is going to happen, but...
If 15% of Tory MPs (or 55) decided that they wanted to trigger a no-confidence vote in Johnson, they could submit that tomorrow, hold the vote on Tuesday, and force a leadership election that day if 50%+1 voted against Johnson.
What happens after depends presumably on how many Tory MPs want to stand for leadership. If there were only one I can't see that there'd need to be a protracted campaign; if not, then the process would take somewhere up to two months.
This won't happen (at least not any time soon), and I don't even believe that it *should*. Better for Johnson to get his act together than for the Conservatives to waste a few months on infighting.