ASA boot sequence is like many any other Cisco devices - POST (power-on self test), ROMMON and then load the OS image according to a combination of the config-register and boot variable values.

I've not measured it with a stopwatch but it's about 2-3 minutes from power off until an ASA is passing traffic. If you have a service module (ips, cx or sfr) those take another couple of minutes to fully initialize.