Thank you for clarifying @enriquedmn, I see that I missed a key detail there!
So the only way I can think to manage this would be to create a custom template for your home page that removes the global header and uses a local header for that page only.
It would be the same as the global header, except using your anchor link only menu.
how to do this will depend greatly on the theme you’re using (custom vs hubspot vs marketplace) and whether you have a child theme (hubspot or marketplace only).
Let me know if you have questions about how to go about this and I can share a few questions I would need answers to in order to provide further guidance.