Is it a well pump motor that you want to start? AC well pumps with a start capacitor and a relay box are harder to start than the type that just have a built in capacitor (permanent split capacitor...PSC). The term "inrush current" is more fitting for a capacitor than a motor. An AC motor has a starting current that peaks right at the start to a value known as Locked Rotor Amps and then tapers off as the speed comes up. If the inverter shuts down when it sees LRAs, it never gets a chance to even try to start. So you must be able to deliver LRA for a half second or so and then sustain something less for the rest of the start.
There are two main type of inverters, low frequency and high frequency. Both produce 50 or 60 cycles but low frequency switch power to the input of a large iron transformer where high frequency work much like a switching power supply. Bottom line is low frequency tend to work better for motor starts.
I have a low cost low frequency inverter that is 230v rated at about 3000w but will deliver about 6000w for a motor start. It started two of my three 1/2hp pumps. The one that wouldn't start had one of those starter boxes and the relay just hummed. Recently I have installed 2, 3000w Growatt (high frequency type) in 230v split phase configuration. I have tested with one of the PSC type pumps and it worked fine.