Hardware Program Management to PM Advice

I'm looking to eventually make the switch from program management to product management. I work as a technical program manager in defense & aerospace & hold a bachelor's of science in business administration with an emphasis in supply chain management. With that being said, I've developed a comprehensive and transferrable skillsets focused around project management & leading cross-functional teams, but looking to further bridge the gaps between PgM and PM. I'm looking to understand from people who have made a similar switch or also come from a non-technical background on what they did to transition into product. I'm currently team matching with Google for program manager positions & I've been interviewing with Apple trying to find a good match as well. One problem I'm running into is that both companies have mentioned that the fact I do not possess a technical / engineering degree is a barrier to the number of PgM positions I'm eligible for despite working as a TPM in defense focused around Mech-E. Would going back to school to obtain a Masters of Science in Engineering help with my ultimate goal to becoming a PM? Or would software development experience / education help more? YOE: 3 TC: 116K #tech #product #productmanagement #programmanager