How difficult it is to become a PMM after MBA without prior marketing experience? What can be done when companies ask for prior PMM experience?

Our PMM intern - who is now a full-time Associate PMM - has this exact background! And we will be hiring another such intern in a month or so! :) 

If you don't have the PMM experience per se, try to do activities associated with PMM work - like creating sales enablement, doing customer interviews, creating sales materials. At a smaller company, many marketing folks have to do it all - so you can start at a place like that and lean into projects that are more PMM-y.

To be completely transparent, I think it's really difficult for people just graduating to come in as an entry level PMM. If that is your goal, I'd think about what responsibilities that typically lie with PMM you could excel at including things like owning competitive intelligence and research or sales enablement. These would be two responsibilities I could see someone without as much or potentially any prior PMM experience being able to contribute to. I'd also consider going into consulting first as this often provides the skillset required to be a really effective PMM. 

This answer depends on what your experiencer was prior to your MBA. If you were in Marketing and/or Product Management prior, you can make the pitch that there i overlap in your past history to connect you to PMM. Or if you are about to start an MBA program, you could look to secure an internship in Product Marketing.

Overall, in general, managers will prefer someone with experience. That said, at some point someone has to get their first product marketing job. The key to that first job in which you have no experience is to network, network, network. Also, there are certifications you can get and being part of communitie like this one and meetups can help.