Science has for its basis the philosophical idea called naturalism. (Consider science's former name, "natural philosophy.") Naturalism is the assumption that we will explain what we observe without reference to gods, devils, ghosts or fairy godmothers. What can repeatedly be observed and measured is the whole scope of discussion. It is a good and useful assumption: It has been a great help, in bygone times, in sorting out received superstitions from actual facts about the natural world. It has also led, in our era, to progress in finding ways to manipulate the world around us: new medicines and materials and machines and marvels galore. (It has also brought us atom bombs, gas warfare and unintended consequences like drug resistant bacteria and ways to die by accident that no one a century or two ago had heard of or imagined.)
Naturalism, though a very useful assumption, is an assumption. That is what we must not forget. By ruling out the supernatural, science can now say nothing about it. It must remain silent on such matters, because the grounds of discussion selected by science have fenced them out.
When you hear science argued as if it contradicts or disproves religious beliefs, the assumption about no gods or devils is being regurgitated as a conclusion. That is not good logic; it is an empty tautology.
The problem is not in logic itself, nor is it a flaw in science. It is a matter of exceeding one's warrant. We know logic is no bar to religious thought; some highly logical theologies show us that. We need a different starting point, that's all: for example, the assumption that the Bible describes reality as it exists beyond our everyday experience. From a truly scientific viewpoint, that assumption is, at best, true but irrelevant. At worst it is false and irrelevant. But science is powerless to say which. How can it?
Divine revelation is a miraculous matter. A miracle, by definition, is not an everyday occurrence, but a one-off event. It is not repeatably measurable. (Notice the same is true if you do not believe in miracles.) But science relies on repeatability of observations and measurements. Something miraculous is, by definition, an exception to the usual order of things. That puts it outside what science can investigate. Science is formally incapable of passing judgment here; it hasn't the tools.
The explanation the Bible offers, for the events it recounts, is inherently outside the naturalistic assumption of no supernatural factors. A scientist can say, quite rightly, that he can't investigate that, using only the rules science gives him. He may say more if he likes, but not as a scientist.
Addendum: A scientist objected to this line of thinking by saying science does not exclude the supernatural. Science can investigate whatever it likes, by an iterative process of observation and description. I am sure he missed the point about miracles being exceptional events, rather than being part of the fixed patterns of the world's operation. There is no predictability to miracles, in the sense that making a study predicting what will happen, and when, will do you no good whatever. There is no opportunity for independent verification by repeating the event and no chance to reproduce the event for further examination.
The example I gave my scientist friend was that of Ezekiel. Christianity and Judaism say that Ezekiel received elaborate visions that revealed things about the purposes of God. It does us no good today to stand where Ezekiel stood and wonder when the next show starts. We have Ezekiel's account and that is that.
Naturalism's unannounced assumption is that the world follows fixed patterns that can repeatedly be observed. It does not deal in exceptions to this rule. I find it interesting that so many scientists feel compelled to speak, mainly in the negative, about religion; it is a subject area that their field of study is unequipped to consider at all.