Try piCore if you want a fast booting Linux.
http://forum.tinycorelinux.net/index.ph ... ,57.0.html
To go faster means optimizing Buildroot
http://www.jumpnowtek.com/rpi/Raspberry ... droot.html
Faster again is baremetal, I prefer Ultibo these days, but it may not yet do what you want.
https://ultibo.org/
I have heard systemd will boot the kernel in about 2secs, the user space stuff takes the rest of the time.
http://intestinate.com/pilfs/guide.html
Less than 2 seconds and you need to write your own bootcode/start.elf.
https://github.com/christinaa/rpi-open-firmware
Of the above only piCore has WiFi support?
Alternatively, start with Raspbian Lite and remove most of the stuff.
And use a A1 rated SD card?