Hello,
To create a transparent header that overlaps the page content we would recommend using of multiple headers option and create copy of the existing header for the home page and edit this copy to change the bg color for the header sections and enable the Header overlap effect for the desktop and mobile if you need.
Watch the video tutorial for the multiple headers option https://youtu.be/BpeXfzNwkOc
If you still have the problem after that then provide us with WP Dashboard access and we’ll create an example.
Regards