At this point, I don’t think that the distro matters much, as there is quite exactly nothing there except for the kernel, udev and the very first steps of startup.

There's the famous "5 second boot" for Fedora on an EEE PC 701. That's a weak machine with a small, old, SSD. It's an "honest" boot time - from power on to desktop up with idle CPU and disk.

(https://lwn.net/Articles/299483/)

Here's an article trimming boot time of Fedora 17 to 3 seconds.

(http://www.harald-hoyer.de/personal/blog/fedora-17-boot-opti...)

There's some overlap between the two different approaches.

If you wanted some esoteric hardware you could make an always powered RAM disc.