Secondly, that tablet has 1 GB of RAM.
That makes it a poor candidate for porting it to UT.

If that is the case then I totally agree with @Moem and would also advise you to forget the tablet unless you feel like learning some new development related skills by porting Ubuntu touch to it!

Moem already answered your question.

I moved this thread to the Off Topic category in regard with this post:
https://forums.ubports.com/topic/206/will-you-port-to-device-x

If you still want to give it a try, you'll find a link for how to create a custom port in the previous link.
You can also check this post for frequent questions:
https://forums.ubports.com/topic/6838/frequently-asked-questions

BR

Mine is now a dedicated device for some games that work best on a somewhat larger touch screen. No internet access of any kind, so who cares whether it's out of support?

Toshiba AT200

Hello and welcome!
First of all, most custom ROMs are found or at least discussed on the XDA forums. If you don't find anything there, chances are that nothing exists.

Secondly, that tablet has 1 GB of RAM. That makes it a poor candidate for porting it to UT. There may be other factors in play as well, but one is enough to say it's never going to be a good candidate.
That means that it's very unlikely that it will ever be ported by someone who isn't you. And if you decide to learn how to port, you would probably not want to waste your time on this tablet.

As for other Linux distros, this is not the place to ask. But for starters, most of them do not run on this tablet's architecture.