This is a big issue, and what follows is the tip of the iceberg.
Start with persuading your organization that a git client is needed on the Windchill server.
Windchill Rehost manual, page 14, URL below:

A similar diagram appears in the System Configuration manual (URL below).
My advice (corrections please) is to look under Windchill/codebase and determine which directories contain configurable files such as XML, JSP, Javascript, and others. Exclude directories with java .class and JAR files. Read about the xconfmanager utility and decide which of its file types (properties, xconf,) you want in git. Maybe have git control of Windchill/bin and the HTTPSERVER/conf directories.
Decide how you will integrate Windchill patch releases and upgrades.
https://www.ptc.com/support/-/media/support/refdocs/Windchill_PDMLink/12,-d-,0/WCRehostUtilityGuide_12_0_2_0.pdf?sc_lang=en
https://www.ptc.com/support/-/media/support/refdocs/Windchill_PDMLink/10,-d-,1/AdminProcessSystemConfigMgmt_139039.pdf?sc_lang=en