Here is where you go wrong in your thinking.
If I were to make the fantastical claim that last night, I climbed up on my roof, flapped my arms, and flew all over the night sky, and when questioned about it said, "You cannot prove that what I have claimed is false", would you accept that what I claimed was true?
Despite the fact that my claims defy the very Laws that govern the Universe?
Of course one cannot "disprove" miraculous claims. By invoking miracles the claimant gets a free pass over the natural and counters any argument with, "you cannot disprove the supernatural with the natural."
Which is why, in the scientific method, it would be up to the claimant to provide empirical evidence of the claim. Without such evidence, the claim can be dismissed as being against known natural laws.
There are many such miraculous claims in the Bible. But to reconcile these claims with science, you cannot invoke supernatural explanations. It is not up to science to disprove the miraculous, it is up to the claimant to provide evidence that the claims are true.
Let me rephrase....
That which is written in the bible can be proven true by science.
You go wrong in apparently thinking I am trying to prove anything to anyone. They can prove it -but how many are willing? I have proved it (proven?). I have not scientifically proven every word of the bible thus far -but I have proven much at which "science" would scoff.
If you do not believe the things therein MAY be possible, your preconceptions would taint any experimentation.
As for that which you can't prove.....
There are actually many scientists throughout the world looking into some very "miraculous" things.
In other words, some very very freaky stuff is happening in the world that important people don't like to openly discuss -but the bible describes it thusly....
Rev 16:13 And I saw three unclean spirits like frogs come out of the mouth of the dragon, and out of the mouth of the beast, and out of the mouth of the false prophet.
Rev 16:14 For they are the spirits of devils, working miracles, which go forth unto the kings of the earth and of the whole world, to gather them to the battle of that great day of God Almighty.
...which may sound ridiculous, but is nonetheless true.
There are many official "programs" that deal with the "supernatural" -but, in my experience, many of those involved do not acknowledge the possibility of said programs being affected by -or even manipulated by intellects superior to theirs -with powers superior to theirs -who lend their power toward their own ends (which -in the case of demons -is OUR end). They see short-term results, and are thereby sold (and blinded to the big picture).
(There are some who do acknowledge the existence of "spirits", but apparently do not understand their nature.)
This brings up an excellent analogy...
The fact that the "spooky people" keep things as hush-hush as possible doesn't mean they're not happening. Most don't have a clue what's really happeneing in the world -as our perception is limited. Yet -given opportunity by permission or chance occurrence -one might prove these things are happening.
Likewise, the things of God can be proven, but he also has the ability to withhold information and opportunity.
In fact, he has set down certain guidelines to follow in order to draw near to him. A scientist would have to acknowledge that this could be a factor.