You need first a DC source with 500 V output. For an "extremely low current" you can use a capacitor charged to 500 V.
From 120V AC, I would use a voltage tripler or a 120V/450V transformer and rectifier diodes rated to ~1 kV.
As "the push button" must not be in the 500 V circuit", you can use a relay to transfer the 500V from the charged capacitor to the load. You can also use a SCR or a thyristor for the purpose, or a HV MOSFET.
As there is no definition of the output pulse shape, no more details can be invented. Also the load must be well defined.
Please be aware that anything connected to 120V AC and generating 500V can be extremely dangerous; people can be killed by it.
I your teacher gave you such task, such person looks to me very uneducated; be careful of such wrong definitions.