So take your 200...
If they build a single city-state like colony, it may be able to survive with 200. If they were able to bring with them sustainable animals, we could see Australia, develop differently.
So take your 200 shepherds and their families, then ... I am no expert on ANE family size, but presume several extended families of two parents and a half dozen of more children; maybe 20 or 30 family units, if that?
If they are refugees/emigrants, presumably they have some connection in the first place, so there's probably some amount of genetic overlap in terms of where they are coming from - even adding in the servants, sailors, odds and sods who end up coming along by circumstance, it's still a pretty small gene pool.
Then they have to - somehow - cross from SW Asia to (presumably) the Horn of Africa/SE Arabian Peninsula, and then (somehow) cross the entire Indian Ocean with no real knowledge of winds, currents, tides, etc.
Then they have to land on a west-facing shore known today as fairly unfriendly to mariners, and which - by the way - fronts some fairly inhospitable desert.
And the fertile spots, are already inhabited by people who are tough, well-adapted to their environment, and know the country.
My guess is the percentage of your 200 who survive (how many months?) of travel and then actually get ashore may be ten percent, or less.
The survivors are promptly picked off by the locals, since the voyagers a) have nothing to trade, and b) know zip about the local country, terrain, etc.
Several hundred years later, when the English or French or Dutch or whoever are exploring, they may note the Yuin or Arunta or whoever have some interesting myths about travelers from the West showing up in the past, but that's about it.
I mean, really, this makes Joseph Smith's version of the settling of the Americas sound rational. At least he came up with multiple waves of Jewish refugees... who all ended up in the Yucatan, somehow.
Cripes, Wilbur Smith's refugee Carthaginians as Boer precursors in the Orange River (complete with proto-Marxist revolutionaries) is slightly more believable.
Best,