As mentioned your best bet would be objects off Earth, though they would likely have to be probes anchored on some stable body. After a billion years almost anything around the earth would have fallen into itshould be lost to orbital decay or to deep space from the steady push radiation pressure from the sun and orbital decay from the exosphere drag. This is a known issue with satellites in GEO due to the earth itself, interactions with the sun and moon, and radiation pressure. Station Keeping is required of nearly all spacecraft in orbit around the earth due to these interactions. Without constant upkeep of satellites and over this timescale it's unlikely that there would be anything to find in orbit around the earth.
On earth actually, you are in luck; there are places on/near the surface that have remained stable for that period of time. It would be possible to find layers of strata that include unnatural minerals or even artifacts from that era. We have left an impression on the earth's geological record even now with the creation of plastics, even minerals, refinement of metals, movement of materials, and interfering with the ratios of radioactive isotopes.