Holding the pedal on the floor while cranking puts the PCM in “clear flood” mode.

If it starts quicker with the pedal on the floor, it may be indicating the engine is flooded.... example - leaking injectors. But the question remains why only on a new tank of gas? Do you tend to overfill the tank? That can cause problems with the carbon-filled fuel tank vapor collection system.

Checking the fuel pressure would be a good first step, as noted in an earlier post. Turn key to “run” (not “start”). Watch gauge to note peak fuel pressure when the pump stops priming (after about 2 seconds pump run time). Should be at least 40 PSI. Then watch to see how fast the pressure drops. Rapid pressure drop can cause extended cranking time.

https://youtu.be/fQG1jThVmwY

The pressure should hold, or drop slowly. Causes of rapid pressure loss:

1 - leaking check valve in fuel pump

2 - leaking injectors

3 - leaking fuel pressure regulator diaphragm

4 ​- fuel pressure regulator not closing off fully, allowing pressure to bleed off into return line

5 - leaks in fuel supply line, including flex pipe in tank

To check #2, pull rails up with injectors intact. Key to “run” to pressure fuel system, look for drips.

To check #3, look for wet fuel in the vacuum compensation line to the fuel pressure regulator.

#1, #4, #5 harder to diagnose. But #2 and #3 could cause a flooded condition.

What code sets when you “top it off”? That would seem like a critical piece of information as to the cause of the problem.