At the time scale of billions of years, the question of whether there was sentient life on Earth is roughly equivalent to asking if there is sentient life on other planets, since Earth is very nearly (but not quite) another planet at that time scale. If sentient life arose that quickly that means it is even easier than we thought it was to arise, by quite a bit. The fact we don't see any in the sky would strongly suggest (but not prove) to me that there was not a previous civilization. (The most parsimonious explanation as to why there aren't a lot of civilizations in the sky is that for yet fuzzily-understood reasons, they can't arise much more quickly. [1])

Plus, while the narrative that "evolution increases the complexity over time" isn't as strong as some may suppose, it does provide a ceiling to complexity over time, and I'd say most of the evidence that we have would strongly suggest that there isn't any feasible way that the biology of a billion years ago could have supported intelligent life, because that ceiling is just too low. Today, there seems to be several possible feasible lines for intelligent life (birds, sea mammals, octopus) in the "short-term" multi-million-year future, with homonids getting there first, but a billion years ago I don't think that was the case. I suspect your average ant nowadays is more intelligent that much of what was around back then.

Oh, and, yes, we could build something that would survive on the moon. In particular, we're not obligated to put only one thing on the moon; that's an artifact in thinking with the exact precise technology of today, where's it's really expensive. In another 50-100 years it's quite plausible that putting up such a momument would be considered on the scale of an ambitious art project, and it's not hard to imagine dozens and hundreds of such monuments being put on the moon over time. Local materials can be used for bulk, and the only upper limit on the size of such a momument would be the energy available for whatever it is you wanted to do with it. Moving around local materials and building the equivalent of a pyramid would be almost feasible today ("almost" here being "less than a factor of magnitude of development away"), for instance, and melting & refreezing mass quantities of lunar surface for some visually-obvious effect is eminently practical if you have fusion. (And if you have fusion that can use the He3 on the moon, downright cheap.) It's not hard to conceive of monuments miles in size, or if you assume self-repairing or -replicating machinery, you can make something visible from Earth feasibly. Even with only solar power, that just slows the project down. Had that been done billions of years ago, some of them (or some of it) may have been destroyed by meteors but the vast majority would still be there. In another 100-200 years of reasonably-projected technological advance we'd be able to consider completely resculpting the effective appearance of the surface of the moon, for any number of reasons and in any number of ways. The moon shows no evidence of this, which would be enough to say that if there is a sentient civilization in Earth's past, it would put the Great Filter back in front of us again. (Albeit much more weakly, since only one civilization may have died before resculpting the moon.)

It's still faintly possible that we'll explore the moon in more depth that we have today and find "something" interesting. The fact that it's soooo untouched at a bulk scale suggests to me it's not likely, but it's possible some civilization got to where we are today, +/-50 years, and then died back, leaving just a trace on the moon, just as we have so far.

(IMHO, the most recent paper on the Fermi paradox from a couple of months ago puts the Great Filter behind us fairly firmly, by showing there's no compelling reason to assume the sky should be full of civilizations.)

[1]: It is well-understood that you need at least some time for complex elements to develop, and in enough quantity to form useful planets and such, so you do need at least some time for some stellar generations, but there is no currently-known reason that I'm aware of that the sky should not be inhabited by a multi-billion-year old civilization. On a cosmic scale, Earth isn't that late to the party in some sense, but looking at its history it still seems like you could shave some billions of years off of its history and still get an "Earth-like planet" somewhere else.