Does it make sense?

Hi all,

I come from a non-target school in Italy (top 10 public schools), where I got my Master's degree in Corporate finance, and I am currently working in the Corporate Finance division of a Big-4. Prior than that, I have worked at GE as an intern for less than a year.
My dream would be landing a job in IB at a bulge bracket bank. Now, I don't know what I should be doing and if applying for a MiM or MiF (I was thinking like LBS MiM) could make sense in my case. I'll be 27 upon start (2019 intake), with a bit more than two years of experience in M&A.
I think that, depending upon the programme, applying for a MiM could boost my chances to get an offer as IB analyst, but I am bit worried about the gap age, not just during the programme but also on the job, and if my profile could actually get the attention of investment banks.
Do you guys think that could it work? I have also thought about keep working where I am for another two years and then apply for an MBA and try to get in as associate. But I am not sure if my profile is good enough to get into a top MBA programme. So I thought it could be easier go for a MiM and then get in as IB analyst.

Thank you very much for your answers and opinions.