Does the cosmological argument rest on the premise that "Everything has a cause"?

Many believe the cosmological argument goes like this: Everything has a cause; so the universe has a cause; so God exists. They then try poking holes in it. If everything has a cause, then what caused God? Why assume everything has to have a cause? Why is it assumed God is the cause? Those who attack this argument never say where they got it from nor quote those defending it. In fact none of the leading proponents of the cosmological argument in the history of philosophy and theology ever argued this: Plato, Aristotle, al-Ghazali, Maimonides, Aquinas, Leibniz, Samuel Clarke, Mortimer Adler, William Lane Craig nor Richard Swinburne. The atheist Robin Le Poidevin, in his book Arguing for Atheism when considering the cosmological argument starts by attacking a variation of the above argument admitting "no-one has defended a cosmological argument of precisely this form." By his own admission no one has ever actually defended the feeble argument in question, but he still calls it the basic version of the cosmological argument. Daniel Dennett claims the argument is the simplest form of the cosmological argument in his book Breaking the Spell. It is akin to attacking Darwinism by claiming the Darwinian account of human origins is built on a monkey gave birth to a human baby. If he provided no source for this claim and admits no one has ever argued it and went further claiming "more sophisticated versions" of Darwinism were really just "modifications" of this claim this would be dishonest and contemptible. The cosmological argument states "what comes into existence has a cause" or "what is contingent has a cause", quite different from "Everything has a cause". Defenders of the cosmological argument also provide arguments for these claims about causation. One may disagree with such but one cannot go on to say God is uncaused.