The dirt that has accumulated over the mosaic is the result of deposition over 1800 years from windblown soil, livestock manure, trash, dead vegetation, knocked-down buildings, etc.
For example in London the Roman level is typically 30 feet below the current ground level. The same is true for the city of Rome as well.
I know...I was just having fun, and you forgot a BIG ONE - volcanic eruptions.
In addition to your list, the high percentage of angular-subangular pebbles-cobbles might suggest sheet wash or mud flows from the surrounding hills. The source site maybe had eroded volcanic deposits or simply denuded soils on those hills.
A seed takes root in a crack between tiles of the mosaic. Roots descend and a green shoot emerges. Photosynthesis begins. Carbon begins being sucked from the air to fuel the plant’s growth. The carbon from the air is used to “build” the plant, and together with water constitutes the vast bulk of the weight of the plant. The plant dies, and its carcass falls where it stood. Repeat 1,000,000,000,000 times and you get 30 feet of dirt.