Slider as background of the logo

Hello,

I would like to have my slider as background for the header, like in this website : https://www.my-vulx.com/
I tried to put my slider shortcode in the element "header", however it displays after my header. I setted the site header to "merge with content", then it was fine except that my slider is too big, so my main menu which is supposed to be below the header appeared in the middle of my slider. I tried to give an height to the header in css on .site-header to match the height of my slider. It works, but now I can't click on my slider anymore.

I also tried it with posting the shortcode in Hooks instead of header, but I can' find a hook that makes it appear as header background.

What should I do ? Is there another way to get the same result as the website I sent you ?

Thanks in advance,

Amandine