Can i make My blog Header like this?

Hi there,

you can use a Header Element:

https://docs.generatepress.com/article/header-element-overview/

This can be used to add the content and merge it with the site header.
Or you can just use it to merge the site header and use a Block Element hooked into after_header to create the content:

https://docs.generatepress.com/article/block-element-overview/