You won’t get automatic admission under the state’s Top 10% Rule (or 7% for UTA), but apparently test scores are a major factor for everyone else.
https://www.texastribune.org/2016/06/23/race-and-admissions-ut-austin-last-five-years/
“…UT-Austin, like many other universities, is always seeking out more students with high SAT and ACT scores. But most of its freshman class is admitted based solely on grades because of the Top 10 Percent Rule. So when the school considers students who are not automatically eligible, it is especially interested in high test scores — and white and Asian students are more likely to fit that profile.”
But with your scores, presumably you do fit that profile. I’d still say it’s a reach but not unrealistic.