Do some rocks, soils, sands or waters exist that contain fewer than one atom of gold per cubic meter or tonne of their mass?
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The average concentration of gold in Earth's crust is about 2 ppb (±0.5, depending who you're asking). This is about 2 milligrams Au per tonne of rock. It's not much, but it still equals about 6×1018 atoms, or 6 billion billion atoms.
Seawater has on average 0.004 ppb of gold. This equals 4 micrograms Au per tonne of seawater. Much less, but still about 1×1016 atoms of gold, or 10 million billion atoms.
So to answer your question:
...contain fewer than one atom of gold per cubic meter or tonne of their mass
The answer is a clear no.
Edit
These seemingly huge numbers do not mean that there is a lot of gold in the rock. That 0.004 ppb of gold which means 10 million billion atoms, is still only 0.0000000004% of the rock. This is clearly a completely insignificant amount of gold. Nonetheless, this insanely tiny amount of gold still an insanely large amount of atoms of gold. There are a lot of atoms out there.
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$\begingroup$ Thank you very much. I wouldn't think how ubiquitous the atoms of gold are ;) $\endgroup$– DanMay 15, 2020 at 8:27
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$\begingroup$ Be careful with averages, they tend to simplify reality. There could very well be a tonne of rock with absolutely zero gold, another one with 4 milligrams, and you'll end up with an average of 2 milligrams per tonne for the two, but you'll miss the fact that the gold is not uniformly distributed between them. $\endgroup$ May 15, 2020 at 12:18
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$\begingroup$ @Jean-MariePrival indeed. But rocks with absolutely zero gold do not exist. And even a rock with 0.0000000004% gold is going to have billions and billions of atoms. Even if you add 10 more zeros before that "4", which is for all practical purposes "zero gold" is still going to have millions of atoms of gold. $\endgroup$– GimelistMay 15, 2020 at 12:57