I know I've herad/read/seen somewhere that the Orions are the oldest spacefaring civilization in the quadrant, but I don't remember where. Might be from ENT.
However, I think that Memory Beta with 200.000 yeas is overstretching it a bit. In my perspecitve, if they've been so advanced and around in the time of the Iconians, their technology should probably be superior to everyone else, which is not the case. Although they seem to be very old spacefaring civilization, thus the ancient secrets that Melanie D'ian offered J'mpok for an alliance and Ter'jas Mor.
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The 200,000 year figure is referencing a thoroughly non-canon RPG game. So it's about as far from 'established Star Trek fact' as you can get. I mean, novels are one thing. . .RPG games are quite another. They tend to be even more crack-brained and weird than novels, though I've seen some really weird novels
As for your question, the article already answers it: "Orion astronauts reached Rigel XIII and studied the superstring over its south pole; with this knowledge they developed the warp drive a thousand years later. With this power, Orions spread out into interstellar space, at around the time that the Iconian civilization fell. They embarked on large-scale space exploration around 200,000 years ago, and became some of the first interstellar travelers in their part of the galaxy."
So, they started exploring space right about the same time the Iconians disappeared. . .in all likelihood, they were using primitive technology that would have posed zero threat to the Iconians, and would have attracted little attention.
PS: In my experience, it's better to reference novels for non-canon facts, especially the newer book series that have been released in the last 10 years or so. Most of the newer novels have been written in a way that's supposed to make them complimentary with one another, not contradictory. . .making for a smooth non-canon timeline/history. Information derived from various RPGs, games, and whatnot tends to be notoriously fractured and contradictory.
Thankfully, CBS hasn't said anything yet, so you can make them as old as you want for your game, or story. (Personally, I'm running with the whole "We don't KNOW how old they are" line-even the Orions have mostly forgotten...)
"when you're out of Birds of Prey, you're out of ships."