The question I'm trying to get at is: from the perspective of the physical realm (which may be, even likely is, all that exists) is there any possible mechanism by which something nonphysical could influence events in the physical realm?

For example, is there any physical property that is not "locked into place" by the laws we know and the observations we can make? Is there any fundamental impossibity (not practical impossibility) of snapshotting the state of the universe and using that snapshot to determine every past and future state of the universe?