I think the solution shouldn’t be imposed upon the team. In extreme cases of PM’s or PO’s imposing solutions teams will start to feel and exhibit code monkey behaviour. Coming up with solutions is (or should be) their expertise. A PM or PO should act as the “customer”, almost as if in an agency <> client relationship.
That said, it’s always a good idea for a PM or PO to “prepare” a little and have your own ideas about possible solutions and be involved in the discussion about possible solutions.