Default Values from context in the same page

I followed this documentation to populate some fields with default values:

https://contactform7.com/getting-default-values-from-the-context/

This worked perfectly if the contact form was on a different page using a link like this:

https://example.es/contact/?service=cleaning

However, I can’t make it work if the contact form is on the same page, I tried linking the form section with an ID, I used a link like this:

#contact/?service=cleaning

This didn’t work. ¿There is any way to make it work?

To put some context, I want to do this because I have various CTA that directs to the same form, but each CTA will populate the “service” field with different information.

Thanks in advance!