There is no built-in way to do that, and no way independent of
org-export to get the numbers, AFAIK.

Here's some ugly old code that shows outline numbering as overlays in an
Org buffer.  It doesn't update automatically, so you have to run it
again when the outline changes.  But it seems to work well.  It uses
dash.el and let-alist, in case you don't have them loaded.