It looks like your javascript (which is formatting your menu) is only running after page load. You have quite a few includes so I didn’t check them all, but make sure your theme is running its setup script on document ready. Like this (for jQuery).
$( document ).ready(function() {
//run script here
});
Also, you could try manipulating the menu CSS. The id for the div around the menu is “sidr”. Try adding “display:none” or “height:0” and see if the menu still works properly.
You could also speed up page load a little by optimising images – you have about 4.3Mb of images on the index page at the moment – which is a lot.