Hi there,
You'd be surprised - this really isn't as big of a deal as you think!
Now, have you missed out on the recruiting pipelines at your MBA (i.e. top-tier companies literally coming to you and begging you to apply)? Yes. Does this mean they value you any less now? No at all!
However, you won't have anything handed to you like during the MBA program
How do you bridge this gap?
Here, I cannot overemphasize the importance of networking, networking, networking. Yes, make sure you have a killer resume and cover letter, but also, network heavily and target a referral.
In terms of networking tactics:
a) Reach out to people in your network - here, you have a huge advantage...reach out to your fellow MBAers, the career office, etc.
b) Reach out to people once removed from your network
c) Reach out to people with a similar backgorund to you (i.e. same alma mater, same hometown, same career switch, etc.)
d) Tailor a message to them specifically both showing interest in them and their journey and demonstrating that you have done your research and could be a valuable hire
e) Play "tag" across calls you get so that you can work your way towards the company/office/role you want
f) Leave a strong impression - i.e. don't ask "basic questions". Rather, demonstrate your ability/intelligence by asking smart questions, carrying a natural conversation, showing genuine interest, etc.