Wait. When did Solas say the other races came after the veil??
I think he says in Trespasser that there were only elves "in the beginning", in the time of Arlathan. The way that statement was made, it's evident it was made on purpose, to lead the Inquisitor to the conclusion that the forced secession between the spiritual world and the physical one caused the downfall of the elves. And such downfall would imply the weakening of their race and the subsequent appearance of other races in the world, disconnected from the Fade and from a spiritual existence; the so-called Tranquil, as Solas phrases it.
But now that you've posed the question, I'm not sure whether it was him who said it or another character, or even it the information was in a Codex. I do remember learning about it in Inquisition, just not where. I'm truly sorry.