Could you clarify what you mean by "my career in SN" - do you mean a position employed in ServiceNow, the company? Or do you mean a vocation working with ServiceNow, the platform?

Either way.. do you need to come from a programming background? Definitely not. Most functionality in ServiceNow requires very little programming knowledge - if anything, the tools at your disposal are very business-oriented and almost make any programming knowledge pretty redundant.

For what it's worth, I teach the Sysadmin Course and out of 3 days there is a half-hour section on areas where scripting is used, and I give a 5-minute brief demo to show anything's possible through scripting, but not everything requires scripting. Most people on the course are team leaders, configuration librarians, project managers, process consultants... there's very few programmers around (or they just avoid my courses).

Definitely look at a sysadmin course as a first taster. It's actually more "instance configuration" than "system administration" - you don't really perform tasks traditionally associated with being a sysadmin, more tasks required to reconfigure and setup an instance to support business needs.