That requires a customized PID 1 init program and a lightweight GUI (that map app is just ~10MiB of code + some code for postgresql that runs in the background) - most of the delay there is waiting for the postgresql to start up, actually.
Arch Linux to some lightweight GUI based on Xorg/i3wm takes about 8s. Similar for my Electron/X11 fullscreen based GUI for the phone (also in the video). Both are much larger.
Sadly, the Linux userspace is quite bloated, and the limiting factor is loading times from storage to RAM. You basically need to load >200 MiB of binaries/.so files to have anything useable running.
With eMMC speed of ~85MiB/s and SD card speed of 25MiB/s max for sequential reads only, you get the picture of where the most of the delay is.
A bit late but thanks so much for this work -- I consider myself a late early adopter and your work is going to make it much easier for me to take these phones for a spin.
https://xnux.eu/p-boot/
I'll make some multi-boot SD card demo image next, perhaps with postmarket, arch linux, mobian and ubuntu touch. :)