I am currently working as a support analyst for an application hosted in AWS.
You might not be ready for the CCSP just yet. The CCSP is almost like a CISSP concentration. It's not a cloud cert as much as a security credential that is very cloud-focused.
If you want to get out of customer support and into security, I would look at something like the Security+. Paul Jerimy has a really good mapping security credentials:
That might help you plan what you want to do. If you want to get some work experience in information security, I'd be on the lookout more for the small company experience where you will multiple hats. You might need to take a pay cut, but if you can tolerate that for few years, it may pay off in terms of experienced gained.