TAMU undergraduate admission is 100% decided by admission office, and upon engineering department request, they look exclusively on students’ Calculus preparedness. That’s why having Calculus to prove is very important. Engineering math is very unforgiving at TAMU, each engineering major easily has over 50 credit hours using Calculus.
At this point admission is not likely. If PSA is offered, consider those five or six engineering majors offered via PSA. If your student prefer other engineering majors, Engineering Academy is another option. I advise against taking Calculus I/II in the summer as such a short time is not enough to build a solid foundation.
PSA engineering option
Engineering Academy