Remove header space on page

Hi, I’d like to remove my header space on all pages except the homepage. After going through a number of codes, the one that worked best was:
.site-branding {
display: none;
}

.home .site-branding {
display: inherit;
}

Although the space is smaller, there is still a gap between the featured image and the menu on laptops (works fine on phone). I tried adjusting the color to hide the gap, but it’s still quite obvious. Anyways, wondering if anyone can give me a hand?

Thank you!

The page I need help with: [log in to see the link]