It depends, pumped storage can be designed to react very fast. In particular pumped storage plants which were conceived specifically to alleviate surge demand can spend a little bit of energy now to stand ready, no longer storing further energy but with their turbines now "spinning in air" the generator is rotating with no load and then when you actually need that power you drop water through to spin it instead, 16 seconds from zero to 6 x 300MW turbines = 1.8GW at Dinorwig station in Wales.
Gas likewise needs to consider this at design time. The most efficient possible closed-cycle gas turbine setup may take hours to be prepared and spin back up from zero, but obviously you would not choose this configuration if your intent was to use this station to handle surges. Britain's fleet of closed-cycle gas turbine power stations (in the same network as Dinorwig) frequently ramp up and down a dozen GW in an hour across the country.
BTW Dinorwig's fast start isn't really there to manage surges, that's a convenient happenstance, nobody was worried about a duck curve from solar power when it was built. It's there because it's a Black Start facility. Most power stations need outside power to start, it's just easier and they're connected anyway, Dinorwig was chosen to be able to start from nothing if the grid fails, so in that sense it's like the box of matches by the furnace, just in case.
Or does it take longer to come online than natural gas?