Can I divorce my spouse ASAP without his consent if he's not a citizen?

You can divorce him; it doesn't matter whether he's a citizen. But it takes at least 60 days in Texas unless there's a good reason for the judge to waive the 60-day waiting period, and his being absent or a non-citizen won't get you there. You'll also have to serve him with the divorce petition, personally if you can find him or by publication if you can't.