When science investigates Creation, it inevitably adopts an attitude of mind limited to what it is studying; in other words its attitude is limited to the created world. Furthermore in order to make sense of what it is studying, science leaves out of account any spiritual element that there may be in the matter it is investigating. It is hardly surprising therefore that the “explanations” that science offers are mechanical, when the whole discipline of the investigation is organised to produce that result. Put simply: the whole business of science is to produce a mechanical account of the universe it is investigating; and one should not complain when it does exactly that. But that does not qualify scientists to pontificate on matters, which they have not even been investigating.
If you limit your attitude of mind to the created world, it means you have ruled out of your mind that it might have been created, in order to investigate how the created world works. Creation is the best evidence of a Creator, as St. Thomas Aquinas sensibly recognised. But in order to see the force of this argument, you have to allow your mind to have a wider attitude than that of the scientific investigator. You have to envisage the possibility that there was a Creator, in order to see if the evidence points in that direction, or not. When a scientist announces that his scientific work shows that there was no creator, it simply demonstrates that he has no understanding of what he has been doing. It is like a lab assistant taking over a piece of research, and because he does not understand much about the subject, he announces that the research is not leading anywhere.
In order to be able to assess realistically whether there was a Creator, or not, you have to allow your attitude of mind to embrace the whole created and uncreated Universe. But since you yourself are part of Creation, that is impossible unless there is insight into eternity, if it exists outside space and time. Goethe thought this was possible by looking into the mind (look within!), and Goethe was usually right. But I doubt if it is possible for ordinary people like myself, unless that person believes he has an indwelling with the Creator; and if he believes he has, that answers the question for him. So we reach the general view that there is no possibility for most people of any proof that God does, or does not, exist. You simply have to make up your mind intellectually, or allow your experience of the numinous to convince you emotionally.
It is little good saying that if you believe in a Creator, the world makes far more sense, than if you exclude the idea of a creator from your mind, because those who do not believe there is a creator cannot view the Universe with a creator sufficiently vividly to compare the two situations. So there is no valid comparison in their minds to enable them to form a rational view. You can only make a valid comparison in practice, if you believe there was a Creator; and if you do, then you have the answer to your own question.