Circuit for helping big motor to launch
No, not really for AC.  That is assuming I understand the somewhat garbled question correctly as "Is there a simple way to help a AC inverter deal with motor startup current beyond the inverter's rating?".

A capacitor could possibly work if the power was DC.  A capacitor can dump a lot of current quickly for a short time.  The problem is that motor startup current is required for a long time relative to what a reasonable size capactor can provide.  Motor startup can last a few seconds, so whatever power source is used needs to be able to provide that.

That all said, if the motor normally requires 500 W, doesn't it startup up well enough with 2 kW supply?  Have you tried it?  It seems like there is a reasonable chance it would work, given the 4x overhead you have.  What voltage?  What is the motor stall current?