The no-miracle argument argues that because scientific theories reliably predict, explain, and control phenomena (including unobservable entities) they must be approximately true rather than lucky guesses. It would be miracle if our scientific theories were as successful as they are yet the world were not even approximately the way our scientific theories describe it as being.
The best explanation for the success of science is that the world is approximately the way that our scientific theories describe it as being. Therefore, it is true that the world is approximately the way that our scientific theories describe it as being.
This argument uses inference-to-the-best-explanation because it assumes that theories are not just occasionally good way of explaining the world, but that scientific realism is the best approach that properly explains the success of theories.
The best explanation for X is that Y. Therefore, it is true that Y
Objection to the no miracles argument = selectionism
An objection to this argument is that scientific theories are designed to be successful in practical ways, so it is not surprising that they are. Some scientific-anti-realism attribute the success of science to natural selection; scientific community doesn’t tolerate theories that fail to make accurate predictions. Another argument is that success is a social consensus relative to different expectations of scientists in different historical periods. In contrast, Popper (a realist selectionist) believes that in scientific selection, weak theories are eliminated and the successive replacement enables the theories to get ever closer to the truth.
There are also questions whether inference-to-the-best-explanation is a good form of argument in the first place and brings it back to the problem-of-induction. There can be a worry that while an explanation that seems best may not be the accurate explanation.