The JobSpy plugin has a tool to run arbitrary programs, not sure if they can be assigned a keyboard shortcut - if not maybe that feature could be added.
Otherwise use the OS or 3rd party tools.
If Windows then:
If you put Firefox as the first to ninth item in taskbar, then WinKey+n key will jump into Firefox (start/restore/bring to top). For me Firefox is Winkey +1, calibre is Winkey+4 etc, viz:
If for some peculiar reason I didn't like that, I would write an AutoHotKey (AHK) script.
Added - or if Firefox is already running use Alt+Tab
I imagine MacOS would have something similar as MS's WinKey+? for its Dock or whatever it's called this week, or you could do it with Automator.
For Linux: IIRC bash scripts can be assigned to a keyboard shortcut, or there's an AHK clone called Autokey, I've only ever glanced at it, its scripts use Python.
BR