Would it be more accurate and reasonable to say "under the Laws of physics, as we understand them today"?

No it wouldn't. The laws of physics have abundant evidence to support them. What you seem to want to do is to invent a new law, for which there isn't the slightest scrap of evidence, that says that all the other laws may be circumvented in order to accommodate your God. We try to get to the bottom of the laws of physics in order to explain the universe as we see it. You want a new law that unexplains everything in one fell swoop, innocent of all evidence. It's so easy to do, isn't it? And cloudy and lazy and intellectually-stunting to boot.