Dan Orlovsky about the saints and Kellen Moore

You're good with these old-time stats; the ones you cite are all at least 30 years old. I need you to update your database. Oh ya, Vermeil was fired, right but won with the Rams a decade later. Also, I said if you did not win by the second season, you're on the hot seat. I fully expect Moore to get at least three years.
They have to be out of football at least 5 years to be in the HoF so they are generally older ...not my call who is or isnt in the HoF. The two most recent of the 13 qualifying HoF coaches are Tony Dungy and Bill Cowher both of which started fairly close to the 30 years ago. So that's really the best I can do.

Bill Cowher is an anomaly and was able to go to the playoffs his first year. He was the immediate predecesor of HoF Coach Chuck Noll which left him a reasonably good roster with HoFers Rod Woodson and Dermonti Dawson.

Tony Dungy struggled his first season but turned it around in year 2. His squad that he inherited from Sam Wyche had 3 HoFers on it Derrick Brooks, Warren Sapp, and John Lynch.

Vermeil struggled his first two years with the Eagles but then took them to the playoffs in the third year and followed up with a Superbowl appearance with the Eagles two years after that.

2 years later the season was shortened by a player strike. Vermeil retired after the player strike as he was burnt out. I doubt the Eagles would have ever considered firing him as he took them to the Superbowl.

He came out of retirement 15 years later and once again struggled in his first 2 seasons.

I concur, A 3-year window is a fairly accurate window for rebuilding with a new coach when your team isnt loaded up with HoFers in most historical cases. So yeah I would go with that.