MOSFET as inrush current limiter (passthrough parasitic C?)
Since you dont have any specs, no solution is [perfect.] = will meet spec.
Perhaps consider a Current sense cct amp. to drive the gate is what you need.
These are just ideas, not proven ccts.
 - i.e. extremely dependent on load, Vt and RdsOn.







simulate this circuit &ndash; Schematic created using CircuitLab

I changed it to a 240mA load.

But in your case, the ESR of your C1 is greater than the ESR of the Miller Capacitance of your FET 

or try this instead to allow slow Vgs turn on.

Rev A







simulate this circuit