IBD advice required

Hi all,
Background: I am in the mid-careers, investment management. I did MSc in Derivative Pricing a few years ago at a target school in the UK. I sadly did not go for a grad role or full time at any of BB. I realised that AI/Machine learning is 100% not something I want to pursue further, regardless, of the organisation. I want to change to corporate finance at the BB. At the moment doing a part-time MSc in Finance (with a focus on Corporate Finance) part-time at a target school (2-years graduation from now with the ability to work because of the evening classes)

Need help with: I was recently offered a position of M&A analyst at a tiny but great firm focused on EM. The firm does not have any network to provide and will provide strong technical skills/ EM (2 countries only) deal experience only. Given that I don't have any relevant experience on my CV and a top brand firm, would it be helpful to accepting an offer? Another option is to push hard and try to get a Financing/Global Markets or whatever you call it job for two years at BB. My target is to work at BB after graduation, hopefully, at an associate level.
The point above is, I tend to recognize that without a BB in your CV, it becomes almost impossible to get a job at BB later on after graduation. So I either take the offer at a tiny firm and get the deal experience or pursue the Financing role at BB. Please advice. Thanks.