Ok, this is how I handled it (thanks a lot to @cmbuckley who pointed me in the right direction).
I created a very simple index.html file in the repository with the TeX project:
<html>
<head>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
</head>
<body>
</body>
</html>
<script>
$(document).ready(function() {
var link=document.createElement('a');
link.href = "EXISTING_FILE_NAME";
link.download = "NEW_FILENAME";
link.click();
});
</script>
Then I set up the repository to serve the branch masterfor the git page. Then I used my own domain and created a CloudFlare subdomain that owns the NameServers of my domain, pointing it to my GitHub page and setting the same subdomain in the repository as my custom domain address.
: , index.html, , , . , , .