I had a similar problem with my 5.7... idled fine, ran fine if I fiddled with the throttle as I shifted into gear and once I got it running over about 1100 RPM. After much fiddling around, I discovered that when I first moved the throttle, there was a very slight, barely perceptible delay in the movement of the accelerator pump linkage. I had just rebuilt the carb (ethanol junk problems). What I finally noticed, was that MERC had painted the carb after it was assembled and installed on the engine. This paint formed a zero clearance bearing on the connection points of the accelerator link rod ( that Z shaped wire rod that goes from the throttle arm up to the accelerator pump arm). One you dismantle this connection, which you need to do to get the top off the carb, the paint gets chipped off and the link connections to the throttle arm and accelerator arm get "sloppy". This allows the throttle plate to start to open BEFORE the accelerator pump squirts gas into the carb throat. The fix, recommended by one of the pros on this forum, was to VERY slightly straighten out the bend in the accelerator link rod so as to take out the slop in the linkage. A very slight CAREFUL straightening out (i.e., make this rod longer) with two pairs of pliers, is all that's needed.
Since this engine wasn't running before, you should also check that the advance springs aren't rusted and the advance mechanism in the distributor moves freely. Remove the distributor cap ( do not disturb wires to plugs) and see if you can turn the rotor slightly, i.e., about 10 to 15 degrees and that it snaps back when you release it.
If it does not move freely, you may be able to clean/fix it if you are handy enough... BTW... there is no "first" in a boat. All boats have fixed reduction transmissions and don't "change" gears ( other than Forward/neutral /reverse).