Is there an Ubuntu-Mate version for Pinebook64?

You have to download Armbian Ubuntu-based test build with MATE desktop:

• focal, 20.04 LTS (!)
• hirsute, 21.04

Reference: related thread in Ubuntu MATE community.

Images for other desktop environments can be found at the bottom of this webpage.

Note that Armbian is not an official Ubuntu flavor and is not supported on this site, but it is almost the same as regular Ubuntu for ARM processors, and most workarounds for Ubuntu would work there too.

The hardware ports available for Ubuntu Mate are listed here: https://ubuntu-mate.org/download/

If there is not one (and there isn't one listed for the Pinebook currently) there's probably no image that'll work directly for the Pinebook64.

You can attempt to use one of the other images, however it's ill-advised as it may cause chaos on your system or brick the device.