The Custom CSS has been set up to hide the header on the homepage.
#collection-60fe53d515592d3e1078688f header {
display: none;
}
Unfortunately it appears some other manipulations of elements at the top of the page are going on in addition. This doesn't appear to be an easy fix without knowing the intent of the original design. Why was the header hidden in the first place? Nothing wrong with hiding mind you but again without knowing why it was done. It is hard to fix.