Quick Open supports fuzzy searching, but as you said, doesn't support files outside the workspace unless they were opened before in that workspace and remembered as "recent files".
The file/folder opening commands like File: Open File...
support switching to a VS Code builtin interface via the files.simpleDialog.enable
setting, which enables selecting files outside the current workspace, and provides suggestions for completions, but currently doesn't support fuzzy search, though there is a feature-request asking for it to: Fuzzy Search in Open File/Open Folder simple dialogs #202367. I suggest that you give that issue ticket a thumbs up to show support for it. You can also subscribe to it to get notified about discussion and progress. Please avoid making noisy comments there like ones that just consist of "+1" / "bump".
So no, I don't think there's a way to get what you want at least without installing an extension. There probably is an extension out there that does this, but I haven't tried any of them. You can search the extension marketplace for fuzzy file openers.