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No machine instantiated in the physical universe is Turing complete in this sense.

You can do everything a Turing machine can do; obviously, you cannot fail to be Turing complete.

We can simulate a Turing machine, given storage. The infinite storage and infinite time is always a sticking point when comparing any real physical system to a theoretical Turing machine, so we tend to ignore those bits.

"Unbounded" is a better term to use than "infinite."

Except that as far as I understand, one of the inspirations for the Turing machine is to explain precisely the computations a human computer could perform with (potentially a lot of) pen and paper.

Theoretically, not in any sense of reality.

And an unlimited life span.