How to see and use Git files in a ftp directory?

I own my VPS server, with of course ftp and git both installed.

Usually, my workflow consists in editing files downloading/uploading through FTP (with WinSCP). I'm new to the Git system and I would like to use it to do web developing in an enhanced way.

I've been able to init a repo inside the root of a website and successfully push/pull/commit changes. What it is not clear to me, is: how can I access those files I'm uploading? I know everything is inside a hidden ".git" folder but it is not physically possible to access them. This makes Git useless for web developers.. But many of them use it, so there must be something I'm missing.

Can someone help me? I couldn't find anything clear elsewhere on the web and I feel completely in stuck. Thank you in advance.