First, 480uF is not a large capacitor.
Most power supplies have a capacitor in 6800uF range after the bridge.
Anyway, you could try adding a capacitor across R1 to slow down the gate voltage.
Edit: Actually, I think the capacitor needs to be across the zener diode.

Refresher:
That circuit is no good as a soft start, because the body diode will conduct, before the MOSFET turns on.
Regarding the place of the capacitor: it will work with it across the zener diode, but between the drain and gate is better because the Miller effect boosts the capacitance, as the MOSFET turns on, so a smaller capacitor can be used for the same delay and it will discharge more quickly, when the power is removed.
Here's a basic soft-start circuit, with an N-channel device to aid understanding. I don't have the simulation handy and will post it later, unless anyone beats me to it.
