Resignation by the end of probation period (PE job)

He's recommending that you find another job, then tender the standard two-week notice to your employer rather than quitting after six months then starting your search for a new role.

I recommend that you start looking now. Buy-side roles at your level of seniority generally take a long time to get into. Leverage your network. I'll paste a portion of a longer reply I made in another thread at the bottom of this post.

You need to a) find people who are receptive to your story (and that's very likely going to be people you know from either school or as a previous coworker) and b) make sure they realize you only want to move, not have to.

If you look like you're in a rush, they'll get the impression you're about to get fired or something bad. If you look like you're simply trying to optimize via a better role, they'll be more receptive. It's like dating; no one wants the desperate person. I agree with the prior poster, you want to secure a new job before leaving your current one.

In terms of approaching headhunters, I believe you ought to try going through your own network at first. See my comment below on how to approach this procedurally.

APAE:

Figure out what classmates are now at shops you'd be interested in working at, and also do the same through the alumni database. Given the caliber of school you went to, this will be a slightly tedious process (over a dozen hours), but you want to be thorough and informed.

Use LinkedIn's advanced search features as well. Don't just run one search, run multiple. For instance, do one search that pairs school and industry ["Private Equity and Venture Capital"], then do another that has school but no industry but a keyword like "buyouts". Then run that with a whole bunch of different keywords to capture anyone who uses different terms on their profile. Then run one for your school paired with each of the top 50 PE shops, then again for the 10 largest VC funds (i.e. the ones that do MBA hiring, like Accel, Sequoia, Bessemer, Bain, A16Z ...).

Keep track of all the names you find in a Google sheet or Excel. Then reach out to people, and keep in mind that this is going to be a 6-12 month process at minimum. That means don't burn the relationship immediately by asking for a job. You need to run a sequence of at least three touchpoints before making any explicit ask.

Reach out by explaining your commonality (school, military, whatever) and industry background to date and asking for a short call or coffee to learn more about what their role is like. At the end of that meeting (whether it was a call or in-person), ask if it's okay to follow up with any questions you have after your meeting. They'll always say yes. Wait two weeks, then follow up thanking them for their time and ideally also offering something of value yourself (a deal lead, a helpful industry primer or report that would normally be expensive, or a book you like).

This is why this takes so long, because it's like dating where you can't spook someone by coming on too strong too quickly.

After a couple of these (e.g. three months), read the situation to see if your vibe is warm enough to comfortably ask if they know of any open roles at their shop.

This is now a waiting game, but since you've hopefully been able to do this with a couple dozen different people at different funds, you've cast your net as wide as possible while still being targeted. This ought to generate several interviews. You'll also get several "We aren't, but so-and-so who was one year ahead of me at school is at X Capital and mentioned they might add someone soon".

In short, the best opportunities come from personal relationships, not a listed process. To maximize your opportunity set, invest deeply in watering your own garden, so to speak.

This is a powerful lesson separate from any temporary need to switch jobs. If you do this proactively, you start to really keep a pulse on what's happening with whom and where. This helps you see more cool stuff for yourself and also be in a position of influence to distribute favors to people you like.

Good luck.