Sticky menu only after header

Website is

I want to have a sticky menu on the home page and have tried implementing the following code:

   @media only screen and (max-width: 1024px) {
      .site .site-header.fixed.float-header {
        position: fixed !important;

With this there are two problems though: The hamburger menu is invisible on white background and the menu is already sticky while still on the header (but only after roughly 100px or so), which looks weird.
Is there any way of having the black matte that usually goes behind the menu appear, but only after the header?

Thank you very much for your great support!

Hello, I’m not sure what exactly you want to achieve.

Can you please provide more details and some explanatory screenshots?

Kind Regards, Roman.