>there's no evidence they exist, therefore is unreasonable to believe they do
That doesn't follow logically. There's no evidence of particles beyond the standard model but it's quite reasonable to assume they exist.
And there is indirect evidence that pop III stars exist. The abundances of light elements formed in the early universe is well measured, there must have been some stars which formed directly out of that producing metals. What they were like is a different matter, but there had to be some first stars at some point.