How would the world look different if many gods (instead of just one god) existed? In other words, can we know from the world itself that only one god exists?
The oneness of G-d is not the simple one we normally mean i.e. one of two; When we say Hashem Echad it is to say he is all there is." One" as appose to limited in any way by any limitations, "one" means he is not dividable or subject to limits. "One" that means Heshem is the Ein Sof = infinite, but infinity we can't understand or comprehend because of the mere fact we are created ourselves. Infinity that encompasses all of creation, infinity that leaves no space free of his existence. Therefore your question does not start. You can see more in the works of the Rambam [Yesodei Hatora, The Guide to the Perplexed]