The shortest term effects are power supplies recharging their capacitors and incandescent bulbs warming up. That's over within a second.
Then it's the motors, which have 2x-3x their running load when starting as they bring their rotating mass up to speed. That extra load lasts for tens of seconds.
If power has been off for more than a few minutes, everything in heating and cooling which normally cycles on and off will want to start. That high load lasts for minutes.
Bringing up a power grid is thus done by sections, not all at once.