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.
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.
I'm not sure that was intended entirely seriously. After all, humans always terminate too...