Getting into big private equity firms

I'm a fairly recent (~1 year) MBA grad from a Canadian School (UBC) with an engineering background. I got hired at a private office PE company in Toronto and I'm looking to make a leap into the bigger private equity firms (ONEX or one of the pension funds in Toronto/numerous funds in New york) in the future (2-3 years) if this firm doesn't work out (I would like a serious salary raise after this time).

Working in a private office as a Operations analyst, I've had/will have the chance to part of the deal team for many of our future acquisitions. I do a lot of financial/operational analysis and forecasting in my work for these deals. However, our company is quite conservative and rarely considers LBOs. They generally buy out the target company with straight cash, and also buy out the target company's debt. They purchase companies for the long term (to keep them instead of flipping them in a few years for a profit). The deal sizes are fairly small because of this strategy. This model is very different than what standard PE firms do, and thus I wont be getting a lot of experience working with the modelling that goes into complex LBOs.

Based on your experiences would you think I have a fair chance at getting into one of these bigger firms? I'm planning to do an FMVA (CFI) certification in order to learn the things I might not learn in this job (link below). Has anyone done this particular certification/ can vouch for its importance ? My other option would be a CFA, but being 28 and already having done an MBA, I dont really want to pursue further education for 2-3 years.

Let me know what you guys think.

P.S this website isn't letting me post the FMVA link.

Edit: For more context, my current firm has an AUM of aroung $750M, deal size $10-$50M. The firms i'm looking to get into are around $30B AUM and larger deal sizes