Very good technical analysis, Elroch.
Though, the thing is, most people "need" a creator even if you could prove through science (but you "can't prove a negative") that there isn't one.
Then, even if you could prove that there wasn't intelligent design (which, again, you can't), we would still have a big dilemma. What was the cause of the big bang? How was the first of the simplest atoms (hydrogen) manufactured?
These would be just a few of the questions. But it becomes a moot point in that most people need (and must have) a creator who loves them.
Pope Francis is either not up to speed with the notion of chemical evolution unless, implausibly, he would count naturally occurring molecules of RNA as "beings" or (less likely, but more valid) he is unconvinced that this is adequate (this is tenable, even if being convinced chemical evolution is inadequate is untenable).
As for where those evolving molecules came from, the naturalistic explanation - that starts with light elements forming in the Big Bang, heavier elements forming later in population II stars and being scattered by supernova explosions, and gravity and friction sufficing to put them where they can form molecules - suffices perfectly.
There was a time when it seemed necessary for humans to have been created, because no-one understood how humans could come from non-humans, it seemed necessary for the Earth to have been created, because no-one could imagine how it came from anything else, and so on for the Sun, the (other) stars - not that any ancient religion recognised stars as other Suns - and so on.
What people can imagine (and then hypothesise and test those hypotheses) has pushed back that which requires a creator so far that it is reasonable to say it no longer necessarily exists.
To elaborate on that, the notion I like best is that naturally true mathematics is the origin of existence, with physicality being how we perceive certain patterns in what is best thought of as a kind of natural information. With this viewpoint, even physical laws do not require a creator, nor does the Big Bang (presuming it is some sort of pattern like, say a singularity of the Riemann zeta function - a very loose analogy with an element of substance).