The Tai Chi diagram should have appeared in the Confucius or post-Confucius period. The name "Tai Chi" was given by Confucius, which means: "It is big and has no outside, and its small has no inside." That is to say: "If it is so big that there is no outside, it is big enough; if it is so small that there is no inside, is it small enough?!"
As far as I know, there was Tai Chi first, and then Taoism.