The idea of the mind being composed of multiple components has been around for all of recorded history.

I dispute that. There is evidence that some cultures had concepts of multiple souls; the Ancient Egyptians and Inuit come to mind. But Greek and post-Greek philosophy and the Abrahamic religions firmly established the idea that humans have a single indivisible ("monadic") soul in all the cultures they pervaded, and that very much includes 19th century Vienna.

So you might say components models of the mind existed, but they certainly weren't "around". Freud might have heard of the Ancient Egyptian concept of the soul but it certainly wasn't something a mainstream scientist could have referred to to credibilitize his theory.