MBB to PE

Absolutely possible. People do this every year, and will continue to do it ever year, but few thoughts: 

1. It is far harder to do then people think. It is pretty easy to go to the H&F , NMC, etc team page and think that its pretty "reasonable" to get a UMM/MF spot. Again, very possible, but people online tend to overestimate how feasible it is. Someone at a MM once told me that the offer rate for any of these PE shops is sub-5% after interviews are given. I have no idea the validity of this statement and figure, but just saying it is not like they are handing out these offers like candy. There are plenty of people who are finance hardos at MBB who strike out. Note that this is reflective of the 2022-present time-frame, might be different if market picks up.
2. You absolutely should do on-cycle, hot take. Fellow consultants tend to advise ya to stay ~3 years in consulting or do off-cycle. What they do not mention is that for some of these bigger firms, then ratings become a big deal. Additionally, getting top bucket at MBB is far harder than you might think when you join consulting. There are a lot of factors out of your control, and it's limited to ~5% of the class. Assuming you have the GPA and school, much better idea to go on-cycle your first year (contingent on getting interviews) 
3. Keep in mind that modeling is very important for mega fund spots, and not something you get in consulting. It is not hard to learn, but you will need to spend time cranking in your free time.
4. Finally, I would recommend you examine WHY you want to go to a mega fund. We have all been there: prestigious jobs are alluring. But its a different thing to read these forums in school and another thing to crank through 90 hour weeks. Whatever the hours you get in consulting are, the hours will be worse in a mega fund role. Additionally, the culture at these places can be rough, so really think through if you are doing it for the "right" reasons. Though to be fair, if you were to say that the earning potential is just so alluring to you that you want to try it out and see if it's for you, I wouldn't necessarily blame you, but just keep in mind what you are signing up for (FWIW,  one of the "sexy" names discussed on WSO wanted to interview me and I turned down because the culture was notoriously bad and I realized through consulting that I did not want that. Yes, it is still unlikely that I would've even gotten the job and I don't think this is super impressive but food for thought).