I was going by the premise of the OP - a civilization that was launching satellites into space. I’d have a hard time accepting the idea of a civilization using only biodegradable materials doing that.
Back then, rubber trees were plentiful and covered the plains as far as the eye could see…
I think there are materials that don’t deprocess. I believe Aluminum, for example, is virtually never found in a pure state naturally. It’s pretty much always in compounds with other elements. But when you do purify it, it can stay uncorroded pretty much indefinitely. A piece of pure aluminum forms a coating of aluminum oxide on its surface and that prevents any further corrosion in the interior of the sample. So if some future geologist digs up nuggets of pure aluminum, he will know that it’s not a natural phenomena.
I thought this thread was going to be about that Ancient Aliens show that was on History Channel a while back.
Voyager 1 and 2 should be around for quite some time unless they get grabbed by a star or planet or something.
You might enjoy reading Stephen Baxter, In Evolution, an sf book, he has a small section on reasonably intelligent dinosaurs, and I believe he posits the kind if civilization you do, wiped out by the bombardment. In “Coalescent” he has intelligent life, nothing like ours, arising in the first few seconds of the universe. He is a hard sf writer, but like the outrageous.
In answer, I suspect we’d never know. The billions of years of the early earth might have been enough time for intelligence to have evolved. We have very few rocks from back then, so I’d guess it is plausible that any traces could have been destroyed by geologic processes. Even synchronous satellites would have been pushed out of orbit by solar wind and micrometeorite hits in a few billion years, I’d guess.
The book is entitled “Life Without People” It’s the same book the somewhat silly discovery show is based upon
It could be The World Without Us by Alan Weisman or The Earth After Us: What Legacy Will Humans Leave in the Rocks? by Jan Zalasiewicz.
The Cthulhu Mythos involves several civilizations, none native to this planet, that predated the dinosaurs. OTTOMH, the Elder Things, The Great Race Of Yith, The Fungi From Yuggoth, and the Flying Polyps. I’ll see if I can dig up a timeline.
The reason they’re exotic in the first place is because they have short half-lives.
There’s many different shades of “pretty much indefinitely”. A decent-sized chunk of aluminum might well survive for millions of years. But when we’re talking billions, it’s probably been subducted and re-emerged multiple times, and there’s no way it’d survive that. In other words, if you ever drop your keys in molten lava, forget about them, because man, they’re gone.
To quote WATCHMEN, “our past would be cancelled. Our struggle from the primal ooze, every childbirth, every personal sacrifice rendered meaningless, leading only to dust, tossed on the void-winds. Save for Richard Nixon, whose name adorns a plaque upon the moon, no human vestige would remain. Ruins become sand, sand blows away…”
(I mean, who needs to build a satellite when there’s already one in orbit, right?)
Jeez. Good for him, though. Thanks for mentioning that.
I just remembered that there was a Star Trek Voyager episode with this premise. Long ago, a species of dinosaur (I don’t remember which one) evolve human level inteligence. For reasons I dare not remember, they left Earth in a vast space fleet.
Ok, first of all, your 2.5 billion year timeframe is well after the last time in Earth’s history that the entire crust was melted or otherwise destroyed. We know this from geological evidence, chiefly the fact that we’ve found solid rocks older than that.
Secondly, you postulate that a race of intelligent beings evolved- at which point I ask, “evolved from what?”. Presumably an intelligent species would be large complex multicellular animals comparable to vertebrates or arthropods in sophistication. Who would presumably have arisen in a complex ecosystem, which in turn evolved from simpler progenitors with a long evolutionary history. IOW, you would expect that their existence would have been proceeded by 500-1000 million years of fossil evidence. Paleontologists looking for evidence of the evolution of modern life have scoured the globe looking for fossils surviving from archaic sedementary rocks, and so far they’ve never found anything more complex than algae that old.
They came from hadrosaurs.
Another fictional example of this is Larry Niven’s The Green Marauder, in which it turned out that nearly a billion years ago there was an intelligent if slow-living (anaerobic metabolism) technological species that was killed off by the appearance of green plants and the oxygenation of the atmosphere.
For something much more geologically recent, the Gandalara Cycle is set in a society of near-human hominids that evolved on the bottom of the dried up Mediterranean, whose civilization and species were erased when it refilled.
2.1 billion though is another matter.
Geosynchronous orbits don’t really last forever, either. They decay somewhere in the order of several tens of thousands of years, due to being perturbed by the Moon, and eventually will crash back into the Earth. I suppose if these ancient dino-astronauts launched something into solar orbit it may still be circulating, but space is really huge and an ancient satellite would be awfully hard to spot.
For completeness I’ll note a dissenting view:
We would have found fossilized tire tracks. 
It’s a while since I’ve read it, but in “The Science of Discworld” by Terry Pratchett, Ian Stewart and Jack Cohen, the authors posit a crab civilisation, long predating our own, of which no trace is to be found in the present day. Of course they are not seriously claiming that such a civilisation existed - their point (as I remember it) is that time is so vast, the duration of a civilisation so short by comparison, and the forces of destruction so relentless and complete that we would expect to find no trace, had such a civilisation existed.