"The Word was God" answers the question of who is the Word, and also the question of who is God. It does not address the question of who spoke the Word; rather, it tells us this particular Word exists eternally without beginning. "The word" here is logos, which was a highly developed concept before anything in the NT was ever written. Treating that whole concept the way you are, with nothing but a modern English vernacular usage of "the word," misses the entire point of what Scripture is telling us.
This is correctable! Here's a little linky to get you started, and I expect others here can point you to resources that go MUCH more in-depth:
https://www.britannica.com/topic/logos
It's understood that the Word came from the mouth of God. You can disagree. But it's my understanding that the Word was spoken.