Video in the header background starts shortly after the image appears

Hey reqonsult,
It looks like that is how long it takes your server to serve the video. I see your site also has many CORS errors for your fonts before the video loads, this could be slowing your site down as it has the also deal with these. It looks like you may have built the site on a temp domain and the fonts are still loading from there, try checking this.
But nonetheless the video loads quickly when I check, if you want to hide the fallback image on desktop for this one page try this css:

@media only screen and (min-width: 768px) { 
#top.page-id-94 .avia-slideshow .avia-slide-wrap {
	background-image: none !important;
}
}

Please ensure to copy the code from the forum and not an email notification so the symbols are not converted.
After applying the css, please clear your browser cache and check.

Best regards,
Mike