A 555 oscillator can drive a voltage doubler. tripler or quadrupler to increase the voltage but the current is reduced. An ICL7660 IC doubles the voltage or makes a negative voltage but its output current is pretty low.
Most Mosfets turn on when their gate is 10V or a little more higher than their source voltage. They turn off when their gate voltage is the same as their source voltage. For a low frequency square-wave inverter two Mosfets can be driven by a CD4047 Cmos oscillator. For high frequency pulse-width-modulation for motor speed control then a Mosfet driver IC should be used to quickly charge and discharge the high gate capacitance of the Mosfets, and to provide dead-time so that one Mosfet is off when the other turns on.
A 2000W square-wave inverter will dissipate about 400W of heat. It will draw 200A continuously from a 12V battery at full load which will cause it to explode. You will need many output transistors, a huge and expensive custom-made transformer and a bus full of car batteries that will take a week to charge. Rediculous.
Some 2000W inverters operate from 48VDC then four car batteries in series last a few hours.