Over timescales of hundreds of millions / billions of years, preservation of an object outdoors in the elements is vanishingly-likely because mechanical erosion and chemical corrosion will attack every substance. In a cave or somewhere else protected, preservation over longer timescales is much more likely.
It's also worth nothing that several billion years from now, the Sun will turn into red giant and the Earth's atmosphere and surface will be vaporized and left as a sterile rock over tens of billions of years. That is, unless we manage its supply of H/He by managing its fuel from burning up too quickly, which could extend the life of the Sun by several to ten billion years. Star fuel management is a difficult but necessary problem for advanced species to solve.
Well for one thing, any ceramic or other durable remnants of a civilization prior to ours would only have had to have lasted for several hundred million years at most, not billions, since before several hundred million years ago life of such complexity would have been vanishingly unlikely or impossible. Secondly, for any prior civilization, the whole sun and cinder thing doesn't apply anyhow and finally, if we or some civilization before ours had vanished, at least some of our durable goods would be conserved in some sort of preserving environment. As another reply here mentions, we have wonderful fossils of some extremely delicate creatures from deep history, a toilet or two would hardly need much to pull off the same degree of conservation and later be discovered. Your notion of it being extraordinarily unlikely doesn't really fit existing circumstances.
> Star fuel management is a difficult but necessary problem for advanced species to solve.
I imagine that's not necessarily true. It may be that advanced civilizations harvest energy from stars, but live in interstellar space ships (which would also explain why we can't spot evidence of them).
That's assuming it would be worth the investment (because systems in most areas of the observable universe can be few and far between) to go to other systems, when you could invest in preserving your own home system by exploring and colonizing planets, planetoids and such around the home-world. When you commit to interstellar travel, you basically need an entire planet's-worth of supplies, energy and biosphere or you send self-replicating robots.
It's not like we can miracle up another Earth or go to another solar system anytime soon. Our best bets are to preserve what we have and have a look at the moon, Mars, etc.
If we had any reason to go there we could build a starship that can reach Alpha Centauri in 100 years or so travel time [1]. Building a ship of a few hundred meters diameter and stocking it with a supplies for 100 years and a few thousand thermonuclear bombs as fuel would be a giant effort, but very doable. Once you have civilization on both ends of the journey you can probably set up a less energy intensive travel method (maybe a scaled up skyhook [2])
Actually, it might be. One solution to Fermi's Paradox is the idea that we can't see other alien species because they're hiding from potential predatory alien species. Hiding in the vastness of interstellar space would in that scenario be a very good move.
Sure, but stars have the majority of mass in a solar system, so you might want to basically deconstruct them to make more ships/habitats. See Orions Arm/deep well industrial zone as an example. :)
It's also worth nothing that several billion years from now, the Sun will turn into red giant and the Earth's atmosphere and surface will be vaporized and left as a sterile rock over tens of billions of years. That is, unless we manage its supply of H/He by managing its fuel from burning up too quickly, which could extend the life of the Sun by several to ten billion years. Star fuel management is a difficult but necessary problem for advanced species to solve.