If they were done supernaturally then would they not, by definition, be supernatural?
No, I don't think so. For example:
Jesus performs a miracle and turns water into wine. Now the water is completely natural. The wine is completely natural. All test show that they are just exactly what they seem to be, water and wine. They are just natural objects. But the miracle itself is supernatutral. It is not subject to test or examination.
What was water is now wine, and the best science can do is say that the cause is unknown.
Aslan is not a Tame Lion