It is important to note that traveling faster than the speed of light is currently considered impossible according to our current understanding of physics. Albert Einstein's theory of relativity, which has been extensively tested and confirmed by numerous experiments, predicts that objects with mass cannot reach or exceed the speed of light. Therefore, it is uncertain if humans will ever be able to travel faster than light.
Speculating about a timescale longer than the time since humans coexisted with Neanderthals, which is estimated to be around 40,000 to 50,000 years ago, is challenging. The future of humanity and its potential advancements are subject to numerous factors and unknowns. It's difficult to predict what technological, scientific, or societal changes may occur over such a vast timescale.
However, it is worth noting that throughout history, human civilization has made remarkable advancements and achievements. The pace of scientific and technological progress has accelerated significantly in recent centuries. So, while we can't predict the future with certainty, it is conceivable that humans may continue to make significant advancements in various fields.
Whether or not those advancements will lead to the ability to travel faster than light, or to the need to survive over such an extended timescale, is uncertain. It depends on various factors, including future discoveries, technological breakthroughs, and our understanding of physics.