I've never seen a satisfactory explanation for how free will can exist, regardless of whether or not God exists. If everything is a chain of cause & effect then everything was predestined by first causes.
You've described what's called a "deterministic universe."
Yes, it's attractive.
And certainly pure free will does not exist. We can easily see some very obvious limits and looking closer see some more subtle ones.
Yet, if we observe carefully we can also observe our volition. We can watch it arise, we can choose to follow or let it pass.
This we can experience directly. As surely as we know our other experience is true, we can know this is true.
(Of course all our experience could be an illusion, but then we could not discuss or debate or trust anything we "know.")
So we have the view of the purely cause and effect, deterministic, universe; and, we have our experience of volition or will. And they contradict.
One or the other is not true, or we have a paradox and the truth cannot be contained in our question.