from what I know about the Big 4 is if you are married to your job for life you will rise regardless of your diploma name (lots of non-Ivy higher ups)
like most mega corporations if you are a company man 100% you should slowly rise, great time to be a 25-40 year old because so many of the Boomers are 65+ now and will be retiring leaving a vacuum for Gen X and Millennials to rise in the ranks a hell of a lot faster than the Boomers did when they spent decades working before rising to the higher levels
(same thing is happening in Law Firms, making partner before you turn 35 is 100% realistic now vs. back in the 80s when the Boomers had no shot due to a backlog of older partners and fellow Boomers vying for the spots)