l have a 2003 5.0 volvo penta.Every ounce and awhile the engine will hesitate or stumble when l accelerrate.It does not happen every time. l noticed usually It will happen if l turn off the boat and then turn it back on and accelerate It usually happens. If l keep on the throttle it will push through it after 10 seconds or so and then be fine, then it doesnt happen untill l turn the boat off again and even then It may still work fine.l suspect l will start by switching out the fuel water seperating filter and the fuel inlet filter.l am also suspect that the relay switch on the fuel pump could be defective.But l figure l would ask the experts on for some advice before l get into it.l would appreciate the advice.

uneven running is probably due to a fouled plug or bad timing. replace the sparkplug. also check or replace the fuel filters.
After that a mechanic is your best bet.

your boat probably just needs to warm up a bit before you full throtle it

Back in the ''old days I'd say ''accelerator pump'' & suggest a carburator rebuild kit.

It is more likely the filter/water separator, & not likely the fuel pump. You also should try purging ur fuel line. It sounds like there is an air bubble in the line. When the engine is running, the bubble gets compressed by the fuel pressure & does not significantly impede fuel flow, but when u shut the engine off, the bubble expands. It takes time to recompress once the engine is restarted; if u accelerate before the bubble compresses, it is too big to allow significant fuel flow.