Credentials? Portfolio link? Internship details?
Kuch to batao...
In general, market is tougher than it used to be. PM roles are in general 1/10 th of SDE jobs ( it is supposed to be like that ). And due to sudden popularity of the role, supply of people looking to get in is actually much lesser than demand ( influencers are the reason to pouplarise this, they are cashing in too... On hope ). Hence they are applying as many filters as they can ( experience, MBA, etc )
I would suggest, get a proper product internship using your other intern experiences and use that for PPO, or get fulltime into a good startup with decent funding ( seed, series A or above ) via a referral/connections.
If you put the effort in right direction, then above should work. Else, tier-1 MBA is always a way.