All human relations have some degree of inbreeding because we share a common ancestor. You may have two parents, four grandparents, and eight great-grandparents, but the pattern can't continue back forever because eventually it'd exceed the number of people to have ever lived; instead, pedigree collapse ensures that, because people are at some point having children with their first, second, third, or greater-distance cousins, the number of required ancestors shrinks again.
To answer this post's question literally, to avoid any inbreeding whatsoever, you would require an infinitely large (or at least 2^(10,000 years / generation time)) population, such that you could always find two unrelated ancestors for any later ancestor, for at least 10,000 years back.
However, it seems unlikely that they would evolve very similarly to humans if they don’t have a sufficient population to prevent inbreeding.
Your problem may be getting them to diverge enough that you can call them "similar" but not "literally just humans". 10,000 years is less time than the divergence between major human haplogroups today. When the Europeans and Americans encountered each other, that was after a lot more than 10,000 years of genetic separation. Obviously culture changes on much shorter timescales, so that part is locked down nicely.
In this case, a small starting population may actually help you, because randomly selecting a tiny gene pool by abducting related humans will cause a founder effect that can amplify minor fluctuations in allele frequencies. That is, genetic traits that are rare (but present) today may be common in the descendants of small, isolated populations. In this case, you can probably get away with only hundreds or thousands of people to prevent the most dangerous inbreeding disorders (see previous discussions like on this post) while still bottlenecking the population enough to cause this. Considering the limited time, though, I doubt this would be enough to bring about something that wouldn't fundamentally be just like any other genetic group on Earth today.