Are the precious metals (silver, gold, platinum) present everywhere throughout the Earth's crust at least in the trace quantities? Do some rocks, soils, sands or waters exist that contain fewer than one atom of gold per cubic meter or tonne of their mass?
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.