You absolutely can, at least in Firefox you can right click on search field, select "Add a Keyword for this search..." Then save it as bookmark and enter the keyword (you don't have to use !, but it is an option if you chose so).
You can also create such bookmark manually and use %s in the url as a placeholder where search query should be placed.
The manual configuration can be useful when there's no direct search field. For example freshports.org allows querying freebsd.org. I can add a bookmark with search keyword "fp" to point to https://freshports.org/%S
After that I can type in address bar: fp lang/python39 to land on https://freshports.org/lang/python39 (the capital %S doesn't escape special characters like /)
You can also create such bookmark manually and use %s in the url as a placeholder where search query should be placed.
The manual configuration can be useful when there's no direct search field. For example freshports.org allows querying freebsd.org. I can add a bookmark with search keyword "fp" to point to https://freshports.org/%S
After that I can type in address bar: fp lang/python39 to land on https://freshports.org/lang/python39 (the capital %S doesn't escape special characters like /)