Summary: maybe a core originating selection pressure that created humanity is the pressure to travel around to ecologically distant areas and exploit the fact that potential prey in those new areas will not be adapted with defenses to hominid-style predation.
An "invasive species" in general is a species that enters a new environment and does harm to the new environment. Here, I mean to point more specifically to the phenomenon of an invasive species that is able to grow quickly by exploiting prey that is naive to the resulting predatory pressure--i.e. prey that hasn't been exposed to hunting tactics similar to the invader's, and therefore lacks defenses against those tactics.
The alien predator niche is a hypothetical trophic niche provided by the totality of all species. More specifically, the niche is provided by the naiveness of every given species to any predators that come from ecologically separate areas. Since any given species is not specifically adapted to an alien species that comes from an area that has long (in evolutionary-change time) been ecologically separate, there is an inherent opportunity for the alien species to invade and exploit the naive native species.
To some extent, predator-evasion strategies tend to generalize (e.g. having acute hearing to detect approaching lions generalizes to detecting any predator). Also, a given alien invader species will have analogs (perhaps more or less similar) already existing in the native area (e.g. hawks moving into an area that has already had eagles will not find rodents naive to aerial hunters). To the extent these effects are at play, the area in question provides less opportunity to possible invaders.
But still, in general, an alien species can expect to find that the local potential prey is less well-adapted against predation by the alien compared to prey from the alien's original home. To redescribe the niche in an inverted way that might be more clear:
Take an ecological area, and a species S in that area. S has some set of predators. The set of S's predators covers some set of predatory strategies--e.g. predation from the air or from the land, predation by sneaking or by ambush or by pursuit to exhaustion, various weapons such as claws and fangs and venom, camouflage, and so on. On the other hand, the set of S's predators will not cover some kinds of predation. For example, IDK, imagine that woodland mice have evolved under pressure from predatory owls and foxes, but have not evolved under pressure from a predator that uses chemical analogs to mouse pheremones to lure mice into a sticky web. For any kind of predation not covered by S's predators, S will not be adapted to defend against that kind of predation; the woodland mouse does not carefully check for visual correlates of enticing pheremones and doesn't know to abhor webs.
So, an invading species that practices that kind of predation will be very successful in hunting S. Now suppose that many ecological areas have gaps in predation-kinds. Then an invader species that either practices an uncommon kind of predation, or else is able to quickly adapt to exploit a non-covered predation-kind, will often meet with success in hunting if it travels to a new area. Thus there is a niche for a predator to continually migrate and exploit prey that is naive to its predation strategy.
Applied to humans: We can hypothesize that humans evolved to fill the alien predator niche. Hominids, on this hypothesis, would continually travel around to ecologically separate areas. On arriving in a new area, a group of hominids would find easy prey (given, perhaps, an ante of work to figure out how to exploit the naive prey). They'd expand through the area (which process would apply selection pressure to learn and apply the novel predation strategy, assuming it's behavioral and learned). Eventually, whether because the prey adapts, the prey is overhunted, or the niche is simply filled by the invading hominids, there would be pressure to continue migrating.
The late Pleistocene extinctions might be some evidence of this. But it comes late in human evolution, so if early human evolution was significantly shaped by the alien predator niche, the late Pleistocene extinctions are an aftereffect, or a last echo of the earlier selective process.