Group the cover element at the top of the page after the header, and then add the class ‘cover-under-header’.
This could be made into a block style.
.site-header {
position: relative;
z-index: 1;
}
.cover-under-header {
position: absolute;
top: 0;
width: 100%;
z-index: 0;
.wp-block-cover {
position: relative;
}
}