Aristotle's natural philosophy was an inquiry into the causal principles of nature. He famously proposed the notions of formal, material, efficient and final causes. At the dawn of modernity, figures such as Galileo and even Newton continued to consider the "causal principles of nature" as the proper subjects of inquiry. Newton said he was interested in the forces of nature (which 'cause' motion), and that he his main goal was "to argue from Phaenomena without feigning Hypotheses, and to deduce Causes from Effects."
At the dawn of modernity, the concept of 'laws of nature' also appears. Descartes was the first to introduce the notion - Newton also appropriated it. However, the concept did not yet have the priority it has today, and traditional Aristotelean causal explanations seem to linger on.
My question is: When in the history of science did 'laws of nature' become the primary/highest form of explanation? When does it become "mainstream" in physics?