I have pondered this question and the first problem that arises is timing. Lets look at the parting of the red sea and assume that the cause was entirely natural from a wind, an earth quake or some combination of forces and lets assume that Lazarus and the little girl were in some sort of coma. The timing of the red sea parting happening at the precise time necessary to glorify God and the healing by Jesus at the precise time to glorify God beg the question about timing.
Perhaps the physical can be explained as the result of natural forces yet we are left with the problem of recognizing that the time and place of these events have almost an infinite probability of occurring without an intelligent cause.
The third problem is the fact that there are witnesses. God may have performed miracles incognito but these miracles were witnessed.
Does pondedring the question in that context produce the same result?
The third problem is the fact that there are witnesses. God may have performed miracles incognito but these miracles were witnessed.
And I'd like to add another to your list: namely, that many people cannot see the forest for the trees.
For example, DNA is a "tree." Information in the cosmos - both in relation to living things (e.g. DNA and language) and non-living things (e.g. physical laws and constants) - is a "forest."
Another example of a "tree" is self-organizing complexity in nature. The "forest" is that order cannot rise from chaos in an unguided physical system. Period. There are always guides to the system. Even at the root, the atheist must admit that space/time, physical causation and physical laws are guides to the system.
There is no physical origin for space/time and therefore physical causation.
Another example of a "tree" is randomness - stochastic methods are highly effective in physical sciences. The "forest" is that one cannot say something is random in the system when he doesn't know what the system "is."
The number and types of dimensions (spatial, temporal) are both unknown and unknowable.
To put it another way, an observer may look at a "tree" and conclude it is not a miracle. But if he could see the "forest" - he probably would call it a miracle.