Well it's hard to speculate from my position, but from checking transfer trends, you need to be better than top 10%; you need to be top 1–3% just to have any reasonable chance.
Suppose you go to Appalachian, for example, the 75ths there are 150 and 3.41. You're in the 90th percentile of grades at whatever school you go to. So what is the 90th LSAT at Appalachian? 155 maybe? That doesn't get you anywhere near UT Law.
Obviously this is a flawed comparison to make, but I'm trying to demonstrate that your 1L grades will substitute for your LSAT score here, but also that the 90th at an unranked school is still so far away from an elite program like Texas because the students are so different. The median LSAT at this example school is 146—that's several points below average.
Percentiles are relative. Being the in the top 1% at an unranked school is still miles behind being bottom 1% at a competitive program.
TL;DR I don't think it's possible for you. I'm sorry.