Realistically, they have a lot less time than you depict, and they won't ever advance past neolithic level of technology. However, they can and will first travel to better pastures, away from harsh winters and towards lush green grass with enough game and fruit to not worry at least about these. But there are enough dangers on the path even there: predators, landslides, accidents, sssnakesss, poisonous trees unknowingly used as firewood (there was a story of a Roman legion that used oleander as firewood to cook food, and died out the following night), floods, flash fires, internal conflicts, etc. And each dead person due to these events would cause depression in the survivors. So, normal people won't survive long enough to develop technology higher than neolithic.
Altering their psychics could help negate at least social problems and general boredom which will settle after a few hundred years without visible progress in technology, but even if you'd put social problems aside, this socium is too fragile to external events to last long enough to employ better technology.
However, there is one path that could help them employ the entirety of their knowledge and get back to the stars:
Human-driven evolution
Aka advanced domestication. They would anyway have to find a stable source of food that isn't plants, be it meat, milk or eggs (or fish, but you can't domesticate fish), so if they would be pursuant and retain enough power over unsuccessful attempts of domestication, they would acquire a herd of some wildlife that could be counted as domesticated; if it's big and four-legged, it could be used as horsepower, if it's pawed, it could be used as hunter-seeker (dogs), if it's bird, it can be used as hunters or scouts (ravens, falcons). With either of those in possession, they should search for animals with big brains and try to make them friendly. Bears, apes, velociraptors, griffins, whatever has a brain larger than a dog's and can be trained to do commands, but is also social and not singular, would do. These should be organized into a herd, or a "tribe" and humans should then follow them together with their domesticated animals, in order to help and monitor their evolution.
If the humans would survive alongside those animals for several hundred years, they would be recognized as something "that's always been here" by that tribe, so they could start influencing the tribe by maybe participating in any activity other than mating fights, or doing something interesting in front of them, producing weird noises but interesting and immediately rewarding results. Doing that for another thousand years might trigger one of the animals to attempt to do the same. In case they won't have suitable hands, they'd have to evolve more flexible paws, which seems plausible especially if/when one of them would succeed at least partially in wielding a stick, which only takes time. Past that, encourage them to both transfer the knowledge on how to grab sticks to descendants, and do stuff with sticks to those succeeding, and in several eons (not sure how fast, as this depends too largely on those animals' paw structure and their ability to ever get upright) the former society would behold their first result of evolution - a tribe that uses sticks.
Past that (and we're already counting eons which are of unknown length), that tribe could be taught to use also stones, in a similar manner, then to use a stick and a stone, then two sticks and a stone, leading to gradual brain evolution in that tribe's members (perhaps with their entire species gaining some as well, otherwise that tribe might get extinct from inbreeding). The crucial moment would happen when there would be a mating fight in which one of the males would use a stick or a stone against the other; here, they have invented weapons. Once there, the gradual evolution would start to happen without direct interference of "higher minds", that tribe and those species would eventually raise a civilization of their own, starting with fire and use of bones as tools, probably up to spaceships in another several eons. And should at least one of those initial humans survive until that, the goal is accomplished. In the meantime the surviving humans might play shamans for that tribe, and since it'll eventually split due to overcrowdedness, the shamans might also agree to split up, sharing knowledge and directing subordinates to not fight tribes led by one of them, making a sort of nation, which might help general survival of the altered animals.
After all, no one really knows why humans evolve from animals, perhaps there was some intervention that made australopiteks use sticks before all other species of Earth (say orang-utangs are quite intelligent but they are still apes, outpaced by Homo) and spread wide enough to survive, adapt and conquer?
