Best pathway to large-cap PE

You could lateral for better exits after first year, although it is doable to go from MM IB to large-cap PE. I was at a run-of-the-mill MM coverage group and recruited off-cycle. Came very prepared when I spoke with recruiters (i.e. had specific geography in mind, type of fund / strategy and had my interview prep down). A few differentiators I thought I had coming from MM was that I had (i) a lot of deal reps after only ~1.5 years, (ii) worked on fairly lean deal teams, and handled a lot of the process execution, and (iii) the first two points allowed me to fully understand the dynamics of a deal and why it made sense, and during my second year as an analyst I started to ask a lot more questions and think about it as an investor. This, coupled with prior investing experience (interned with an endowment during undergrad and was also heavily involved with a student-run equity fund), allowed me to stand out. I could speak eloquently about all of the deals listed on my resume, what my role was, and how I personally actually thought about the deal / if it was good or bad. I think this is often an overlooked part of prepping for recruiting. Of course, the modeling is also very important, but at the end of the day most people can learn that with a little bit of prep and hard work, especially coming from banking or consulting backgrounds. They don't want to hire execution monkeys, so seeing how you can think critically / form opinions about the deals you've worked on, and other general investment topics, are a big way to stand out. Went through the full recruiting process for an UMM's large-cap team and explained how I was interested in the complexity that comes with larger transactions (working on carve-outs, P2Ps, and the like), and that I wanted to become a well-rounded investor. Also genuinely had interest in the firm's approach / prior deals and wanted to stay in PE rather than just doing a 2 and out type program, which also helped me stand out in conversations with seniors. 

Of course, take all of that with a grain of salt because recruiting has so many variables, many of which are out of your control. I got the offer with the UMM and had a few other interviews with decent MM funds but also got passed on by several smaller funds. Had interviews where I thought I crushed it and then got radio silence, and vice versa. It's a difficult and often tiring process, especially compared to recruiting for banking during undergrad when you have a lot more time on your hand, but for me it was well worth it and have found the work to be more interesting while being surrounded by a better team. Your MM group was not the same as mine, so I don't know all the dynamics, but the best thing you can do to position yourself is to have a really strong reason for why you want to pursue it, have all the modeling and interview prep down, and take a targeted approach to recruiting and speaking with recruiters (think about geography, sector, or strategy). Lateraling could certainly provide more / better looks at large-cap teams, but it's up to you to determine when the best time and place is to approach recruiting. 

Best of luck.