KW is the wrong question. Look at current capability.
The motor will have a full load amps rating, the VFD should have a maximum current rating, plus a rating at 150% and maybe 200% rating, both of which are short term, the 150% is often a 1 minute or so rating, and the 200% may be as short as just a couple seconds.. Those are typical rating points, but the limit is a "current-time" limit that can be tripped by any prolonged current over the continuous limit.
You are not likely to get a VFD rated at less than about 40% of the motor full loaf amps to really even spin it, because the motor takes about that much at idle (at a very low power factor so low watts), and there is bound to be some drive system friction that needs more current/power, plus you do have to speed it up, drawing more current.
If you mess around with the accel time, you may get it going. The VFD usually does NOT have to supply the 5x current at start, because it brings up the speed slowly, and does not supply full voltage to start.
There is a balance point between a too slow start, and a too fast one. Fast does pull extra current, in fact ALL acceleration does. But the 150% short term can carry you through that if not too fast.
If the accel is too slow, you may time out by being within the current limit, but drawing it for too long. So sometimes a faster accel will not go over current, and will last a short enough time to avoid a timeout problem.