Since you will be a senior this fall you have very little time to accrue some engineering ECs without having it seem like you are doing so only for the sake of your application. It won’t seem genuine, and other applicants will have activities they have been competing in for years. If you were a junior I would suggest taking a summer engineering program, which would give you a real sense of what engineering is all about. (There are many mentioned under summer programs on CC.). It would also have given you some concrete experience in the field to include in your application.
You can certainly try building a case for yourself and apply to Viterbi. Your college counselor can give you some good advice on tailoring your application. However, since you say you are strong in math and science, you might consider applying to USC as a math major, or one of the sciences that interests you. If you conclude that engineering is for you, then you can apply to transfer from Dornsife to Viterbi. That is possible at USC, unlike some other highly impacted universities.