Are you using a plugin named rocket (probably the caching plugin)? Looks like it is filtering all the scripts for some reason and causing some form of error leading to home page not showing up when the site loads first. Actually the site does load fully but the page loading icon never goes away which is perhaps due to a script alteration or error ( I do not see any error). Can you pls disable this plugin and instead of use WP Super Cache and see if that helps improve the situation?
I do see that scripts have been executing a bit slow on your server too. When I run a performance profile on your server, most of the CPU is being consumed by two scripts cloudflare.min.js and rocket.js, which are not part of theme itself. Can you pls make changes accordingly and see if the situation improves?