Prior to the Council of Elrond and the proclaiming of Aragorn being the Heir of Isildur, is there any backstory information on how they met? Perhaps they could have run into each other on a hunting mission, crossed paths somewhere between Rhovanion and Gondor or Eriador?
No, there isn't.
In fact, there's no indication in the text that they have met before the Council of Elrond, although it does seem likely; Aragorn delivers Gollum to Mirkwood before the events of The Lord of the Rings:
Gollum, however, was before long captured by Aragorn, and taken to Northern Mirkwood
Unfinished Tales Part III: "The Third Age" Chapter IV "The Hunt for the Ring"
That's the first time we know of where it's likely they could have met, but there's no indication that they did.