Intermittent fuel issues

My car has an SR20 engine in it. Its a drift car. I am having a problem with startup. When I activate the fuel pump before cranking it works and I get pressure, but as I turn the key I lose most of the pressure and it the pump works under powered almost. Car just swings and swings until it kills the battery.
When the car does eventually start after lots of patience it runs perfectly fine with no power loss. This problem is only on startup and done with fully charged batteries.
Please help. Lol