We originated from a space-faring civilization. A breakaway faction that hates advanced space level tech traveled here and set up shop before destroying their advanced tech. They were unprepared for the large animals on Earth before the Ice Age and they quickly lost the ability to make any reasonable tech. A few generations later and they were unadvanced. They retained their ability to solve problems though and eventually out competed the native proto-Hunan Neanderthals.
In 3096 we have reached interstellar travel using a combination of wormhole (govt. access only) and considerably slower warp drive. We send colony ships out and quickly find that we are totally surrounded by alien colonies. We soon find out that these aliens are genetically related to us.
While some conspiracy nuts (yes, they still exist in 3096) expected this, most of humanity is shocked. The aliens are genetically different from us in many areas however as they have had to use gene manipulation to adapt to new worlds.
My main character falls in love with the High Princess of the alien empire (which is by its own nature peaceful). They decide they want to escape the obvious difficulties that would be caused by their union by fleeing known space. They want to have children.
How much genetic variation would allow offspring? The offspring do not have to be viable from the standpoint of reproduction.