30 seconds should be long enough for it to start pumping. It won't be pumping a lot of psi but I would think it should be pumping within that amount of time. Typically it won't start pumping immediately on a cold start.

Does your boat set out? Could be other things as well, check the pee hole and make sure it's not clogged. Wasps and other things like to nest in there and clog that line up.

Worse comes to worse they're relatively simple to change yourself, lots of places to get step by step process. A mechanic is going to charge you $60 - $75 per hour plus the part.