Here's a thought that relates to Mathematical Induction. Let's accept that mankind is near to having the ability to terraform another planet, and make it suitable for human colonization. And that in time, civilization will develop in such terraformed entities, and some will themselves develop the abilities to terraform and colonize. It takes so long they will have no cultural memory of their beginnings, perhaps some ancient lore or mysterious aritifacts.
Let's go back one step instead of forward. Isn't there a very high probability that we are the result of terraforming and colonization?
the problem with spreading terraforming across the cosmos is the amount of materials you’d have to drag along. this makes it almost prohibitive.
that being said, it’s possible ‘seed pods’ could be sent out, pods that would find a suitable location and start the process.
of course, it’d be very wasteful to spew seed pods across the universe, hoping they might find a suitable planet.
instead, the builders would probably use the gate system to transport the seed pods to planets found to be suitable by the cheaper, more expendable, searcher drones.