This is more of a hrair problem. Most people have never knowingly encountered a million of anything at once (though of course everyone unknowingly encounters far more atoms than that all the time), but they can extrapolate that far. Taking a million
of a million of something just requires a bit more extrapolation than someone not used to working with numbers can do automatically.
People do usually understand these things when put in terms of things they have encountered. Say that a million seconds is about 11.5 days, that a billion seconds is about 31.7 years, and that a trillion seconds is about 31.7 milennia. Most people will at least see the first distinction, and at least have some notion of the second.