Maybe I misread your reply, but to be clear - you apply to Texas A&M University (step 1) then your application gets forwarded to COE (step 2) for holistic review, you will get an answer from COE ( College Station campus, Blinn Engineering, Galveston Engineering) , ( step 3) Then YOU decide: accept given path to engineering or pick another open major at College Station campus. IF you select COE, you will take courses and then apply to your specific major at a later date within COE - you can change your mind as to which major you want to apply to within COE.
PS - to my other fellow posters, if I’ve got this wrong please correct me 
The pathway to an engineering major has changed quite a bit in the last several years.