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I'm not sure what you mean or intend to do. Git is not a software integration tool, Git is a revision control system designed to track development changes throughout the software development lifecycle.
If you wanted to use git to pull and push a standalone copy of a filemaker file for working amongst a pool of developers and tracking versions, then theoretically it is possible.
If you want to push said files to a hosted enviroment with live data, then it's a bit more of a challenge (requiring an MVC / data separation style of development ).