Predicting the future of scientific and technological advancements is highly speculative, and it is challenging to make accurate predictions about specific breakthroughs or capabilities that may be achieved by humanity. However, it is worth noting that the timescale since our last common ancestors with Neanderthals is estimated to be around 600,000 to 700,000 years ago.
Given the vastness of the timescale involved, it is difficult to project with certainty what advancements may occur in the future. It is conceivable that humanity may achieve significant scientific and technological milestones within a similar timescale, or perhaps even earlier. However, it is also possible that certain limitations imposed by the laws of physics or other unforeseen challenges may prevent us from achieving certain capabilities, such as traveling faster than the speed of light.
It's important to acknowledge that our current understanding of physics, particularly the theory of relativity, indicates that faster-than-light travel is highly unlikely to be possible. However, as our scientific knowledge expands and evolves, new discoveries and paradigm shifts could potentially open up new possibilities or reveal previously unknown phenomena.
In summary, while it is difficult to make definitive predictions, the timescale since our last common ancestors with Neanderthals does provide a significant amount of time for potential advancements. Whether humans will achieve faster-than-light travel or other extraordinary capabilities within that timescale remains uncertain and highly speculative.