The youngest Partner at McKinsey I know was 31 years old at the time of promotion. That's really a fast track and an exception case. Normally, it takes at least 2 years being Analyst, 2 years Associate, 3-4 years EM, 3-4 yr Associate Partner, so totally it takes 10-15 years for top performers to reach Partner level.
What does a Partner at McK, Bain or BCG do btw?
The answer is they do 3 main things that CEO of most companies do: Sales, Team & Stakeholder Management.
To even reach Partner level, you need to bring in and retain 2-3 big client- companies willing to pay MBB team million USD for each project. These are usually big MNC, bank, conglomerate or state-owned companies. Partner' sales work include building the network, speaking at conference, publishing research & industry report, and doing free diagnostic projects for potential clients.
At this stage, Partners probably spend no more than 20% of their time on the actual project's work. They spend more time managing key stakeholders, the senior people from client sides like CEO or Board Directors. One funny story is my EM one time telling me Andy (of course not his real name)- the Partner will just join our weekly call and say general stuff like "when do you get it done", "good progress so far" and "is there anything I can help". A lot of times, they don't know the details, and actually they don't have to if they assemble a strong project team. And that starts with the Manager, who will then assemble a team of Associates and Analysts.
How's it different from the work of MNC or corporate's CEO, we can talk about it another day. But similar to IB, MBB has multiple partners who actually own shares of the firm, so it's more a flat hierarchy.