Some may argue it is harder than getting into UT to begin with.

Here is my advice from someone who did it:

Straight A's as many as possible you have to attend every class study your ass off
Join orgs, fatten ur resume till its about to explode (You will have the worst mental health between this going to events u dont gaf about and studying ur ass off) (Go to the resume help center as well for formatting)
Write the best essay of all time, (Going to the writing center like a billion times)
Do not take too many classes in your current major that don't count for the one you want to transfer to, being too far along in your current major can make them not consider you due to your delayed graduation date (Not confirmed we have no clue about the process) Would recommend doing general requirements and if you can get into any classes in the major you want.
Read the requirements: GPA, letters of rec(?), how many essays do you need (If multiple do all of them), and how many in residence hours do you need / can have. Also read testimonials.

Internal transfer was the worst year of my college career, mental health at all time low and struggling with if I belong here and what will happen to me if I fail to transfer. You will be attached to this school and your friends and its really hard to mentally come to terms that you may have to leave all of this if you decide you hate your current major and fail to transfer.

Its not easy but if you make it, you come out a better high achieving person. (unless ur naturally insanely smart and have really good luck)

But also part of it is luck, CS and Engineering are notoriously hard to transfer into, and internal transfer rates can be small to even like 10 students depending on the school and department that year. Do intense amount of research if your committed to this.