Except for some high end electric
toilets that use onboard pressurized fresh water, marine
toilets aren't designed bring water into the bowl and hold it because water in the bowl will end up all over the head when the boat heels or gets bounced around by rough seas or wake.
So a cup from the sink is the easiest way to add water to the bowl ahead of use...nt necessary ahead of liquids, but definitely recommended ahead of solids because some water in the bowl leaves it and the toilet discharge hose a lot cleaner without all the extra pumping that fills up the tank with flush water. There's no need to completely fill the bowl...somewhere between a pint and quart should be enough.
If adding water to the bowl makes the toilet flush easier, it sounds like the pump
is in need of lubrication. There are two ways to do that: flush about a tablespoon (any more will be wasted) of vegetable oil
every 2-3 weeks, or only have to do it once a season by taking the top off the pump and squirting about a tablespoon of thick silicon or teflon grease (the same stuff that's in all manual toilet when they leave the factory) into it...replace the top, pump a few times to spread the grease all over the inside of the pump and you're good to go till next spring when you lube the toilet as part of spring recommissioning.
And about a cupful (more of that would be wasted too) of distilled white vinegar flushed once a week, followed by about a quart of clean FRESH water after about 45 minutes will prevent sea water mineral buildup in the toilet discharge line. Do NOT leave vinegar sitting in the bowl! It'll cause the joker valve to swell and distort.