How to Gow as software tester

A certification like CSTE gives basic to advanced level perspective on Software Testing Career.  Generally people who have done CSTE would qualify to lead or manage software teams.

Another aspect of software testing is Automation, one should know what can be automated to save the recurring project's testing costs.

BA(s) may or may not be expert testers.  In my opinion BA is more of a functional expert then a software testing expert.

Growth path could be Software Tester >> Lead >> BA or PM

ANother path could be  Tester CSTE >> Add QA skills like CSQA >> Lead SQA for a huge project >> QA head of company.