Alternate OS image on an open board. This is not Android/Magisk root.
How-to
How to
Write the OpenWrt / Armbian / Arch Linux ARM / postmarketOS image for this exact board to microSD (or eMMC) and boot, per the source pages; open board, no bootloader unlock step.
Follow the specialist sources linked on this page. If this path is a jailbreak, unlock, or flash, the specialist wiki is the how-to — we do not copy those steps here.
Notes
Olimex's product page names A13-SOM-512 and states OpenWrt support. Armbian's board config covers the 256 MB and 512 MB modules under the A13-SOM family name.