But if you have other evidence (besides the current Sys Admin experience) of developing / improving the infra of a product-led startup/company or doing automation etc. - which had positive impact on the users / product performance - it may work. I’d refrain from using Sys Admin evidences, and try to gather as much as possible from other kinds of technical contributions and outside work conferences, mentoring, articles etc.
You might want to use DevOps / SysOps engineers since OS engineer might be the persons writing Operating systems - not quite sure what TN refer there.
As for evidence, it’s pretty similar to other tech roles - do you have large projects that you worked on? Can you show impact on your org? Do you have evidence for contribution outside your work?