The world wide planetary production of tritium from natural sources is 4 x 10 to the 6th power curies per year with a steady state inventory of about 70 x 10 to the 6th power curies. If that helps.I wonder how much of that actually makes it down to the ground though.
Such an interaction produces tritium atoms, probably radicals, that would need to bind with something relatively heavy to make it diffuse into the atmosphere. If it does not react it will escape the atmosphere since it is light enough to do so (like helium or molecular hydrogen).
Honestly I am not sure how much of the tritium found on the surface of the earth and the oceans actually is from cosmic ray origin. I've always understood that the very vast majority (like 99+%) of tritium in ocean water and such was produced by nuclear bomb tests.
Afaik the amount of tritium in a sample can actually be used to determine age to some dergree, at least to something being older than the massive scale nuclear tests in the 1960s or thereabouts.
The natural steady-state global inventory is about 7.3 kilograms (kg).
After being produced in the atmosphere, it is readily incorporated into water and falls to earth as rain, entering the natural hydrological cycle.
Here is a whole nine yards about it including environmental concentration--is a pretty good article on it--
see: Tritium and the environment