Fighters who had the deepest quality of wins prior to winning their first major world title

Jack Johnson & Sonny Liston.

 

Prior to beating Alan Minter for the title, Marvin Hagler had beaten Bennie Briscoe, Willie Monroe, Bobby Watts, Cyclone Hart, Sugar Ray Seales, Mike Colbert, Kevin Finnegan and Johnny Baldwin. Not to mention a draw with Vito Antuofermo. Not too shabby.

 

Harry Greb is the obvious answer!

Greb took the middleweight crown from Mickey Walker in his 280th(!) fight - and had before that defeated 13 future HOFers, a total of 30 times. A clear "winner" of this question!

 

He took the crown from Johnny Wilson actually, but that was still after he'd already beaten the likes of Tunney, Loughran, Gibbons(es), & a host of others.
(Note that he did win American recognition as LHW champ from Tunney, but that doesn't fit into the OP's criteria for a major title.)

SRR would be a close runner-up IMO - wins over the likes of Armstrong, Zivic x2, LaMotta x4, Angott x3, Servo x2 before ever getting his 1st shot @ a title.

 

Shame, shame on me for making a mistake like that!

Of course Greb became champion by beating Wilson. This blunder will be hard to live down... so it'll probably be some time, before I dare to show my face here again!