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.
mike-0ac22.el
Description: ap/org-outline-numbers
