From the point of view of genome comparison the signature would be unmistakable, as @user438383 has pointed out in their answer. There may be however other methodological issues undermining this study:
- Scientific - one need an attested representative of a Jewish genome from 2600 ago or their attested ancestors
- Political/religious - genetic testing is not recognized as a valid proof of Jewishness/non-Jewishness by Jewish communities (see, e.g., here)
While the scientific issue that I mention might not seem as much of a problem, the experinece shows otherwise. E.g., the highly controversial hypothesis of the Khazar ancestry of the Ashkenazi Jews has been a subject of much debate, with many studies both proving and disproving it. Khazars were a people and an Empire to the South of (modern) Russia that were an important political power throughout a few centuries. They are known to have converted to Judaism (or at least their elites). However, as this culture had vanished about fifteen hundred years ago, one cannot attest which people are descendants of Khazars and what genetic signal is an evidence of such a descent. Affirming or disproving this hypothesis is thus dependent on what is taken as a Khazar genome, and arbitrariness of such a choice produces equally arbitrary results.
This is to bring precision regarding some of the remarks made in comments.
- Firstly, to quote the OP:
Would 2600 years be enough time to erase all genetic evidence that this population originated from Israel Jewish people?
- To summarize my answer in more plain terms:
[..] comparing two genomes proves nothing, if one cannot attest their origin. Jewishness issue was mentioned in passing, as a kind of things that a scientist needs to take into account, when posing an answerable research question.
- In more expanded terms, as requested by the author of the OP themselves:
- This would not prove that they are Jewish, since there were many other peoples present in the region at the time. 2) Over the two-and-a-half thousand years the region has been subject to many mass migrations (note that this is a land bridge between Europe, Asia and Africa), so it would be likely controversial and dependent more on historical than genetic evidence. Each can have his/her own point of view, but proving something beyond any doubt is next to impossible.
- Finally, discussing "what/who is Jewish" would take us far away from biology, since it involves intertwined religious, ethnic, cultural, and historical aspects. The only reason to mention this in this context, is that a scientific question should avoid such complex and ambiguous notions, since they may render it unanswerable.
Seeing the number of up- and down-votes to my answer, as well as the comments, I would like to add a bit more rigorous discussion regarding the difficulties involved in such a study. There are three points that one needs to address:
- Do genomes of relatives separated by 2600 years still resemble each other?
- What are the genomes that one needs to compare?
- What does the positive/negative results of such a comparison proves
Point 1. is easiest to answer: yes. One could do a back-of-the-envelope calculation that 2600 years is about 100 generations, which means about the same number of new mutations in a 3 billion nucleotides long human genome. Recombination poses a greater challenge, but we still expect to be able to compare chunks of genome of tens or even hundred thousand nucleotides long. This perhaps already answers the OP, and this is why they accepted the answer by @user438383
Point 2 can be addressed in (at least) two ways:
- Proxy genome @user438383 pointed out that a Canaanite genome is available. If we do find the similarities between this genome and those of our target group, this counts as a result. But if we don't, it again proves nothing, since the ancestors in question could be from a very different ethnic group. Note that we are talking here about a land bridge between Africa and Eurasia, through which the ancestors of most of the non-African human populations passed at least once.
- Phylogenetic reconstruction @KonradRudolph mentioned phylogenetic reconstruction, but didn't elaborate. To implement such an approach we will need to
- sample genomes from the populations that we believe to descend from the Middle East
- build a time-labeled phylogenetic tree, to prove that the most recent common ancestor is located somewhere around 600 BC.
- Prove that this common ancestor actually comes from the Middle East
A correctly posed scientific question of this type should not make any reference about Jews and should not draw any conclusions about them. Doing so is just bad science. Indeed, Jews is a complex term that may refer to
- certain ethnic groups (more than one) - vision widespread due to some sad historical events
- religion - anyone can become a Jew by converting to Judaism, and such conversions are known to have happened on a large scale - e.g., the Sabaean kingdom, occupying a part of Arabian peninsula (modern Yemen) and parts of modern Ethiopia is known to have practiced Judaism, and some of their descendants in the region are continuing to do so till these days.
- Cultural, political, and other attributions (e.g., Soviet Jews had it written in their passport, even if being non-religious and having rather remote Jewish ancestry.)
It also has a more direct bearing on our question, since it doe snot allow us to attest the ethnicity of the founders of the community in question, nor do the members of thsi community need to be descendants of its founders.