Earlier quoted context omitted.
Are you sure about the few minutes part? The standby generators I've seen take seconds to go from off to full load. We have an 80kw model, but I've also seen videos of load tests of much larger generators and they also take only seconds to go to full load.
It might depend on when the backup system was built. No company updates their system every year. A few minutes seems correct for one place I worked. This was back in the 90's, before UPS technology got really interesting. Our system was two large rooms with racks and racks and racks of car batteries wired together. When the power went out, the batteries took over until the diesel generator could come online. I saw it…
The "when" shouldn't really matter- Diesel engines aren't a new thing. Warming them up isn't really a thing either- they'll have electric warmers hooked up to the building power to keep them ready to go.