Great question! Becoming a Computer Science Support Specialist is one of those fields where there are many different paths you can take to get there. I got a job as a Technical Support Engineer after going back to school for a Post-Bachelor's in Computer Science. (I already had an Economics degree and wanted a career switch.) I got the job after completing about a 1/3 of the classes required for the CS degree, which gives a pretty solid foundation for Support roles, while giving me some on the job experience to work towards a Software Engineering role. I know others that gained jobs in Technical Support by going to Code bootcamp or teaching themselves via online resources. That said, what really matters is practice, working on a portfolio and showing enthusiasm for learning! :)
If you want to become a Computer programmer, the 4-year CS degree is a great way to go.
If you want to get into a Support field, Code bootcamp, 2-year Associates degree, etc should be good.
I suggest spending some time defining where you see yourself - IT help desk/System Admin with hardware is different than say, Computer software / QA / debugging code.