Not an exciting answer, but yes 737 is the fastest way to get there.

I believe the most junior guy on the July vacancy was hired early this year. Just know also if a vacancy popped up in a different aircraft and your seniority would hold DEN in that different type, you could always bid into the base that way (unless it was 737FO to A320FO or similar, going uphill in size or seat you won’t be seat locked).