By definition, divine intervention is the intervention of the supernatural into the natural created world. It is true though as CS Lewis points out, that this supernatural intervention does not break the laws of the natural world only speed them up a bit. Still it is the intervention of the supernatural into the natural world.
I’m not going to argue the point, and I wish I could recall the book in which Lewis made the point, but I cannot. I’ll simply leave you with the same question Lewis posed, and it made a very profound impression on me, so I will assure that if it’s not verbatim it’s pretty close:
“What could be more, ‘natural,’ than that which existed before all else?”