First let me answer the original question:
Do I need to have a background at coding if I want to study computer science?
Absolutely not.
About 25–30% of computer science majors at Illinois were admitted with zero programming experience. Those students have to work a bit harder in the introductory classes, but after a few semesters, they do just as well as the students who were coding in the womb.
The updated question has a slightly different answer:
Should I learn programming before starting to study computer science?
That’s not possible. Starting to learn programming is starting to study computer science. It’s not the only way to start learning computer science, but it’s almost certainly the most common.