Lateraling to MBB/How do I get outta boutique?

Wanted to get some no-BS input from folks who’ve been in similar shoes.

I recently accepted a Strategy Analyst offer at a boutique consulting firm, mid-market clients), strategy/implementation focused. It's not name-brand, but there’s real client exposure from what I have heard where they put jr folks in front of clients and give you more ownership.

Context: I tried to break into MBB and failed. I go to a non-target (satellite campus) where consulting exits are almost non-existent. Our main campus might be a semi-target for UG, MBA people definitely place pretty well in MBB. LinkedIn searches turn up nothing from my campus. To date, I only know of two people from my school who made it:

• One is literally at the same boutique I’m joining, same office, joined a year before me.
• The other went Big 4 advisory post-grad, and only just made the switch into a consulting role. They also graduated one year before me.

So here's what I’m trying to figure out:

• How does starting at a boutique like this position me long-term (MBA, corp strat, buy-side pivots, operator roles)?
• Does the lack of brand tank chances of pivoting into MBB or even tier-2?
• What’s the actual path to move up/out from a boutique, and what should I be doing in year 1–2 to keep doors open?
• Any examples of people who made a strong jump from this kind of background?

Not looking for sugarcoating, just want to make sure I’m thinking ahead and setting myself up right.

Any insight would help, thanks.