Hi, yes it is possible. In order to shift to management consulting or strategy, you need to start prepping for case interviews and guesstimates in order to excel in the interviews. You could read up cases on the websites of top consulting firms to get more idea about the management strategy domain. Even better, you could do an internship in this domain too hoping for a PPO. Stay active on LinkedIn and use your personal connections. Hope this helps.

Considering how open management consulting is to freshers and to aspirants from diverse backgrounds, making a switch to management consulting from product management wouldn't be a problem and would actually be an advantage since this would be your specialization