Not a Texan, but here in Missouri, you can request your absentee ballot as early as 9/24 this year.
I requested mine, waited two weeks, and it never arrived. So last week I requested another, and I'm waiting for it. I do think there's some fuckery afoot with the mail, so I'm probably going to be stuck voting absentee in-person at my local election board.
At the same time those Republicans who they'd hope to gain support from by allowing to vote by mail now believe that voting by mail will lead to fraud.
Honestly early voting isn't too much of a pain. I already know I'll be out of town for work on election day but because of early voting I'll be able to get it done before then. It's silly how complicated a process they make registration and how most of the polling locations are churches, but allowing voting by mail won't fix the main issue here, registration.