Since (past time) ... to (current time)?
I am trying to write a sentence that shows my experience as a cook; for example, since my first job at ABC, and then to DEF, to currently working at GHI, I have gain ...
Solution 1:
“Since my first job” refers to a time after the job ended, suggesting that you gained no experience in that job. Better to start with something like:
Since starting my first job at ABC I have worked at DEF and GHI, and have gained experience in ...
This is only one of many suggestions you may receive but it avoids the awkward start.