Humanity just disappears tomorrow, let's say it is like the Thanos-snap but it kills everyone. How long until the last unambiguous evidence of our existence has disappeared? What was this last relic?
The faint spectres of electromagnetic signals which will travel space for ever, odd isotopes ratios and material compositions and slightly odd geological patters are not considered unambiguous. A Voyager probe which still looks like something designed by intelligence and not like a very metal rich asteroid is unambiguous.

Assume that another civilisations exploration mission with near future tech and the capability to launch such an expedition to examine the solar system for 100 years comes looking. They got time and huge resources on hand and will study the major objects until they know about them as much as we currently know about Earth.

Post-Edit:

With orbital multispectral imaging available there is no way that any remains of our cities will be missed, some of those remains won't last long, geologically speaking, but others will last through multiple cycles of super continent formation and break up. These traces will be small, relative to the scale of modern construction they represent, but unambiguous, grids of mathematically straight lines many miles across where old road surfaces interrupt soil formations and buried walls and rubble piles disrupt plant growth. The cities that last the longest are going to be the ones that are in the middle of the continental building blocks know as cratons; Alice Springs in Australia and Hyderabad in India are prime suspects for leaving traces the longest as are Moscow, Riyadh and Brasilia. Those are probably going to be detectable, at first scan, with current/near-future technology while the world lasts, with a century to scan and check data I'd consider it a near certainty. Unless there was another heavy bombardment, that would almost certainly cover up all evidence of human habitation.

Pre-Edit:

The last thing to go will probably actually be Mount Rushmore it's solid, meta-static (meaning in pressure equilibrium and not subject to foliation erosion), granite in a geologically stable region with reasonably stable continental weather patterns. I've never heard an estimate for how long it will take to be unrecognisable but I have seen it estimated that it definitely will still be recognisable in 1.42 Billion years time. This is long after Voyager and the Moonlanders are expected to have been destroyed by micro-meteor impacts, neither of those, nor Neil Armstrong's foot prints, are expected to last until the next super continent formation in 100-200 million years.

probably longer than the earth has.

Fossilization is a thing, and we have set up many things in perfects places to be fossilized. We bury things in salt mines, seal things in glass, bury massive amounts of garbage in anoxic conditions, etc. On top of that we have built things that will leave traces for billions of years, chernobyl will stick out like a sore thumb, much like how Oklo did when it was first discovered, but the composition of materials will make it very obvious it is not natural (corium). Oddly some of our oldest inventions will be the most obvious Stone tools and fire. Humans have created a lot of fires but often in small isolated stone lined pits, these will be very obvious markers in sediment for billions of years, even more so when combined with obsidian fragments and cut bone. Even things like buildings can "fossilize" that is get buried and preserved, exposed building will not last long but someplace like pompeii or missile silos built depositional environments wi last as long as the rock in those areas do.

Then you have the direct evidence from out own bones, humans are everywhere some of our bones will fossilize and some of those will will have dramatic evidence of technology. Not just the evidence from out anatomy but things like false teeth, polymer and ceramic implants, glass eyes, plastic buttons, glass lenses, etc. One fossilized humans skull with ceramic dental implants will be unambiguous proof of a technological species. So not only will they know a technological species existed, they will have a decent idea of what it looked like.

The only way to destroy all this evidence will be to destroy earths surface geology which means liquefying the planet which is unlikely to occur before the sun explodes, or even for a while after that.

Mega Construction

We build, not just cities, There are dams huge chunks of smooth cement laced through with even grids of steel. The edges of the Hoover Dam and Three Gorges Dam and Aswan Dam will be there long after the rivers run dry.

Mining

We dig. There is an open pit mine 3 miles long, 2 miles wide and half a mile deep. It's not the only one. There are similar mines on every continent except Antarctica. The sharp edges of the mine will eventually erode but the shape of the land has been indelibly changed. The spacing of the mountains and ridges will be inconsistent.

Satellites

Satellites in Geostationary orbit are up there for millions of years. If aliens come along they will see a large number of items floating suspiciously close to a synchronous orbit and careful collection should find something relatively intact.

Space Probes

Most of the above should be detectable until the sun starts to expand and swallows the earth. There are currently 5 space probes which have achieved escape velocity from the solar system. They should be observable pretty much forever.