It takes a while to fill the tank, and there usually is a bit of trapped air, that has to work its way out.
When I fill my water heater, I open the pressure relief valve. This appears to purge more of the trapped air at the top of the tank, than just running a faucets.
As for the pump, there is no difference in getting the trapped air out than being connected to city water.
Fyi, never run you heating elements unless there is sufficient enough water in the tank, or it will overheat and fail.
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