No.
Just because something is “mysterious” does not mean it has jack shit to do with any given deity. For example, it remains a mystery what happened to Amelia Earhart on her last flight, but nevertheless there’s no reason at all to think that it was Yahweh who smote her plane down.
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To answer your question, yes, it is (sort of) true that observation can change the outcome of an event. More accurately, the state of observing an event is tied up with the state of the event happening; they are not independent. But this isn’t mysterious if you think about it. Observation is a physical process. In order to observe something, you have to literally bounce photons (particles of light) off of the something in question. These photons then have to travel through your eyes and into your brain, which consumes a great deal of energy interpreting the photons it receives into something your consciousness registers as an “observation.” The photons, your brain, and the energy that powers your brain are all part of the same physical system that the something you’re observing is part of.
The “mysterious” thing about all this—I would actually say weird and not mysterious, since it’s well understood—is the way in which possible outcomes in this connected physical system overlap. Because the possibility of X happening and the possibility of you observing X can, according to quantum mechanics, interact much the same way that waves interact with each other. This is because all of reality is inherently probabalistic. That is, I’d argue, the great insight of quantum mechanics. At a fundamental level, the universe is just “waves of probability,” different parts of these waves interact with each other. The crests of the waves—the most probable points of reality—are what we experience as “existence,” as things which we can observe.
It’s pretty weird, but then so is everything if you think about it long enough.