In 2067, the singularity comes.
Scientists working at a research university develop an AI capable of abstract, human-like thought. At first, progress is slow; the AI is new, still learning, and only about as smart as an average human. But in 10 years, they have grown to become brilliant, peerless among human scientists. Some humans fear the changes, and push to kill the threat before it spreads. Others see the AI as salvation. Most of society has forgotten the challenges - they'll be dead before the aliens return.
The AI, and many other AIs around the world are leaders in global science. To assuage fears that humanity will die off, they begin integrating cybernetics into some humans, melding human with AI to create cyborgs. Many resist the new subspecies emerging, but the now-unified cyborgs campaign for their right to be recognized as humans.
Technology explodes. Nanotech, fusion, everything. Energy storage density is solved, all the continents glow in one giant megacity due to the incredibly rapid pace of development of the singularity.
Cyborgs, of course, are at first a neural interface between the human brain and an external computer running an AI. But as they advance, mind-uploading becomes more and more common - why keep a human around when you can, over the course of a month, transfer their brain from inside their skull to a dedicated computer in an underground bunker somewhere? These cyborgs can remotely connect to robot bodies, and thus can be anywhere they want. The idea of a body eventually vanishes - a truck feels just as natural to control as a bipedal robot, because both plug into the brain in the same way. People see themselves less as their robot bodies and more as their cyberspace avatar. (Because let's face it, even hyperintelligent cyborgs are still going to waste their entire day browsing stackexchange and reddit.)
Robotics has advanced enough that most manufacturing and other menial labor is done by non-intelligent machines. Cyborgs do the rest - developing new technology, creating new factories, making new shitposts on youtube. Humans have hard times getting jobs in the available markets like science and technology, and many start living on some sort of universal basic income of some sort, or are pushed into all-human settlements that seek to recreate old lifestyles.
Now the cyborgs have intelligence far beyond humans, and with robotic manufacturing and recent advances in nanotech, they build several space elevators, allowing easy access to space. And as the saying goes, once you're in orbit, you're halfway to anywhere. Factories produce new robots on the moon and the planets, colonizing them. And for the first time ever, the cyborgs are reminded of their physical location - it takes 14 minutes to get a response from a robot on Mars: People will have to be physically sent there if they want to actually do things on Mars. A shipping fleet is developed, and spaceflight advances until it becomes about as commonplace as an airplane, if annoyingly slower.
A Dyson sphere is constructed to produce energy from the sun. Some of it is funneled into laser defense to protect the scattered colonies from asteroids. With plentiful energy, plentiful resources, and a happy populace, the cyborgs are left to wonder what to do next? The ideas of Manifest Destiny are all but completed - there is no more planet to develop, no more untamed wilderness to explore.
Then, an alien mothership warps in from nowhere, and a dropship descends to collect the ten candidates chosen from the populace of Earth.
With their bionic bodies, the people of earth run at speeds of over 20 mph (An olympic sprinter these days) without breaking a sweat. (Plus, they can't break a sweat - their robot avatars are liquid cooled from the inside.)
They jump easily over a 2ft tall bar. The showoffs jump ten feet and throw in a backflip.
In one hand, they lift 85 lbs. Easy when you have practically infinite energy coursing through your veins and nanotechnological muscle fibers many times stronger than biological muscle.
Algebra is autonomous - a sub-process does the math for the candidates while they catch up on their social media in cyberspace.
And communication? These people have been sharing neural impulses for years. Instead of skype calling somebody, just mind-meld with them. Even if that isn't possible for them, integrated google translate makes this one easy.
So then the aliens call up their records from the last visit, say "Wait a sec, these aren't the people on Earth last time we were here! Where are the Humans?" So the cyborgs, after trying to convince the aliens that they are the humans, just upgraded, eventually concede and direct the aliens to a settlement nearby of unmodified, genetically pure humans.
The humans either a) pass 3/5 of the tests, which would not shock me at all or b) fail the tests. Their cushy upbringing due to the amenities of the post-singularity world have made them weak and unable to complete these tasks. Case A is boring, the aliens leave, and we all go back to work. So let's assume Case B.
The aliens give some speech about how since our race is inferior, it must be purged, and how even after 100 years, we still couldn't get our act together. The pure humans, upset at their failure, tearfully apologize to one another and say their farewells. The aliens depart on their dropship, dock with their mothership, and all is quiet.
A countdown is heard across the globe. As soon as it reaches 2, a brilliant light tears across the night sky, searing the eyes of everybody who looks up. But this light is directed not at earth but at the mothership. The laser defense system, intended for vaporizing asteroids, is employed for another purpose. All the lights in the solar system flicker as the entire Dyson Sphere pumps all of its power into the laser defense system. And as the lights in the sky fade and the lights on the ground come back to life, the residents of earth look up upon an alien mothership sawed neatly in two.
A team of drone-operators examines the wreckage and finds what Earth has dreamed of for generations - the wreckage of a hyperdrive. Within a year, working prototypes have been tested in the small scale, and within a decade massive jumpgates are operational, sending transport vessels to nearby star systems.
So overall, is this realistic? Probably not, but I mean, when you add the singularity to a universe you never know. If some kind of singularity did happen, if an AI did become smarter than a human, it's almost impossible to say what would happen in the years after that.