If it was an alias/shortcut/link to your Bookmarks file in the Brave/Default folder, the original file should still be there, but it sounds like that’s not what it was.
If it was a bookmark file on your desktop that you put in the Trash and then emptied the Trash, you’re going to have to use something like an undelete utility to get it back. If that’s the case, it’s probably going to be much easier to revisit the links and rebuild the file. If you can’t do that, use the disk it was on as little as possible. Emptying the Trash just deletes the record of the file; the data should still be there as long as the system hasn’t overwritten it, yet. Or if you have “secure delete” enabled, it is probably gone.
There are many tools available to undelete files, some free, some paid. Here are some articles about data recovery and tools for doing it: