You brought up infinite machines, hence my and the other person's comment. Turing computers or machines have infinite tape. Maybe you meant to just say "computer," not "Turing computer."
Humans can use computers but only for human readable tasks. There is no guarantee that we could comprehend a superintelligence running off a supercomputer, we already don't understand neural network internals at even their current stage.
I meant a general purpose computer I the sense of a universal Turing machine, but without the infinite storage requirement. Technically that would be a linear bounded automata, but that glosses over the the universal construction of the Turing machine.
Maybe the norms in HN are different, but in my field a Turing machine is primarily a general purpose computer, and “Turing complete” describes models which can represent any Turing machine within its constraints. An “infinite tape Turing machine” is explicitly specified when needed.
Personally I’m a bit outside of the mainstream in that I never use infinities except in the case of representing an unterminated series. I reject that “infinity” as a number even makes sense as a context.
Human beings have access to the same amount of storage and processing power as AIs, because we get to use computers too.