... used in a stand-by mode with a near instantaneous startup
IIRC, from 0 RPM there is a couple minutes to spin up. This is demonstrated in some of the truck videos as well.
There is a lower-power "idle" speed that can be used for faster ramp to full power.
Anyway, the "correct" solution might be to have two-minutes or so worth of storage to provide power from worst-case scenario.
Batteries, compressed air, ...
Heck my semi-engineering mind even suggests using the generator as a moter to spin up the turbine very quickly, using power from the storage. But might run into thermal-expansion issues from "thermal shock" and uneven heating of parts.
There would likely be some enhancements to support the potentially higher torque applied to shafts? Maybe not if the rate of acceleration is tightly controlled.
Bill