Site homepage not available

First, check your site at Securi (to see if it was hacked). If not, consult your webhost. This is assuming you made no changes to cause this.

I am not sure what type of diagnosis your host was able to provide you… Did they test the live site? Did they note they also received 403 errors? Did you make any site changes lately including updates?
Without a site link, we would only be guessing at the issue.

Change the permissions on index.php back to 644.

We won’t know until you try. Troubleshooting is a process of elimination.

Then he needs to look at possible file ownership issues. This is a hosting issue – not a WordPress one.