Jadnashua
Retired Defense Industry Engineer xxx
If the fill valve was replaced (or it's misadjusted, on those that can be adjusted), it may not be filling the bowl up before the tank is full. Check to verify that the hose that directs water to the bowl is properly fitted and is filling the bowl. It sounds like the first flush leaves the bowl fuller, since it doesn't actually flush properly. Then, the second flush works because the bowl is full.
To test this, note the water level in the bowl, then take a bucket and slowly pour water into the bowl. If it goes up, AND stays there, that is the problem, you need the valve to put more water into the bowl. How you make that happen may mean buying the manufacturers valve, or finding one that is adjustable so both the bowl and the tank fill at the same time to their proper level. Or, buy a new toilet that works out of the box that will use less water (maybe a new Toto?).
To test this, note the water level in the bowl, then take a bucket and slowly pour water into the bowl. If it goes up, AND stays there, that is the problem, you need the valve to put more water into the bowl. How you make that happen may mean buying the manufacturers valve, or finding one that is adjustable so both the bowl and the tank fill at the same time to their proper level. Or, buy a new toilet that works out of the box that will use less water (maybe a new Toto?).