There are VFDs on the market that accept 120 volts, single-phase as input power and produce 3-phase, 240 volts as maximum output power. They presumably have an internal voltage boost circuit. There is plenty of online information describing voltage boost circuits.
If you can get 240 volt, single-phase, note that virtually all VFDs convert the AC input to a fixed DC voltage. Therefore using single phase input for a VFD that is designed for three-phase input is usually a matter of determining how much the rectifier needs to be derated when only two thirds of the rectifier is in use. Also the DC bus filter capacitors need to be evaluated. Many manufacturers publish the rating for single-phase input at the normal input voltage. Some who do not will provide the information upon request. Others have design details that prevent single-phase input.
You can make an estimate of the derating factor based on assuming the current per input phase does not need to be reduced. That would make the derating factor 1/ square root of 3 = 0.58.