From what I know, you’re supposed to create a template, and in the template type you need to select “Error Page,” and then click edit with bricks on the template, create whatever you want to show on the 404 page, then while you’re on the bricks editor, go to settings > template settings > conditions > set the condition to “Error Page.”
Not sure if this possible, but why would you like to do so?
The Error Page is shown if someone enters a URL that doesn’t exist. The permalink of the Error Page itself is never visible in the address bar of the browser. It shows always the wrong URL you enter. So if you for example enter something like https://someurl.site/thispagedoesntexist/
that URL stays in the address bar of the browser - not the URL of the template. So it really doesn’t matter which permalink is used internally.