Here is one topic that is describing what you are trying to do. Getting the right terms for searching and for the operations in a design program can be a challenge to learn.
Fill the shape you want to be the background.
Make your text and other design.
Convert text to path. In Inkscape you ungroup too and the combine all the lettering and design you want raised.
Select the design and then the background too. Then Path Difference.
Something like that. Check the tips and tricks section for more help