FTP and GitHub sync?

Question

FTP

Good evening. The essence of the question is as follows, you need to synchronize FTP data (site files) with the GitHub service. There is an idea how to do this, but I'm not sure if it's correct.
The idea is as follows. There is a website on the hosting and access via FTP, we download all the data from the hosting to the locale and work with them, after any changes we send the changed data to the server. After the end of the edits, we send the melons to Git.
Is this the correct approach, or is there some other way?
Thank you.