The only problem is in the use of the word “exist”. It has many meanings. Existence of a mathematical constraint on an abstract system, is not the same as physical existence in our universe. In the former sense the patterns exist but not at any time, it is a timeless existence. In the second sense the patterns demonstrably do not exist (physically), of course assuming that they indeed do not exist (you forgot to say anything about that).
I think it gets more interesting when we know the patterns that will emerge, and where these patterns are the thoughts of a machine intelligence, recreated by starting with a particular recorded state, and applying recorded inputs and forward evolution. This can be viewed as just a simple way to force the electronics to certain predetermined, known states, but it is the same going on as in an original context where we recorded the state and input signals. And in that original context, we were certain that there was a mind.
And instead of asking about the existence of the patterns, in abstract mathematical or physical sense, we can ask about the existence of the mind here: it existed earlier, in some sense of "existing", and with now exactly the same going on in the machinery, except that we know that state evolution and are effectively imposing it, is the mind's "existence" re-created?
I would tend to say yes wrt. to the inputs being applied, but this is a hard one.