Gas peaker plants
are designed to be turned on and off regularly. They can go from cold shutdown to full load in less than an hour, with some able to do it in less than 10 minutes[0].
A decent bunch of that is going to be sheer inertia as you have to spin up a heavy chunk of metal. Keep that rotating (which is actually a good thing in renewable-heavy grids!) and it can be done even faster. Similarly, keeping some parts warm costs very little energy and allows even faster ramp=up.
But that's actually not relevant because battery storage is far more attractive for that kind of short-term demand. The renewable grid will need gas plants which can fill in the gap left when it is both dark and wind-less - which due to meteorology is trivially known 72 hours in advance, leaving plenty of time to prepare the plant for use.
[0]: https://www.eia.gov/todayinenergy/detail.php?id=45956