1/2 second run out of water

If 1/2 a second is anywhere near actual, you probably didn't do any damage.

I would use the garden hose "Ear Muffs" to get water to the engine and start it up with the COVER REMOVED.

Watch the weep hole for the "tell-tale" stream of water to confirm that the pump is working. This is not a 100% guarantee but at least an encouraging sign. If you have real high water pressure and a tight fitting ear-muff you could force water past a bad impeller.

So.... if in fact you do see the tell-tale stream let the engine run for a period and feel around on the engines water jacket for hot spots, it should get no hotter than you can comfortably stand. Use your fingers cautiously at first so if it is real hot you don't scorch a finger, or a inferred digital thermometer. If there is even the 1st hint of paint becoming overheated and smelling, or the engine is warmer than you think it should be, turn off the engine immediately and replace Impeller and Pump Housing.

I would next make a special trip to the lake on the least busy day and back the boat into the lake enough to cover the cavitation plate a couple of inches, being certain that the prop will not hit the boat ramp and start the engine. Leave boat on trailer.

Start the engine, with cover off, watch for telltale stream and again feel and check around the engine power head block for hot spots.

If it passes these test and does not at any time activate the over-temp warning signal, you probably lucked out. With the cover still off make an actual boat ride test at idle speeds and if still no overheating gradually increase speeds in modest steps checking temp constantly.

If all of this passes, thing are most likely OK.

I indicated a quiet day on the lake, and I would not take the whole neighborhood for a day of boating, this it a TEST day only.

For the first few times of actual boating be extra alert for an over heating problem and do not turn the boat over to someone else to operate unless you are in the boat being alert for the overheat risk.

Don Dando