Winter season in central/southern Italy is mostly characterized by high levels of rainfall, and this regularly causes multiple high water level events in the Tiber.
In today’s Rome, 40 foot retaining walls exist to protect the most vulnerable areas of the city from damaging floods, however these were only constructed in 1876-1926, following a particularly nasty flood of the Centro Storici in 1870.
You can actually see the high water point on these walls in this picture (darkened stone):
https://i0.wp.com/www.liquidadventuring.com/wp-content/uploads/2015/05/Tiber-embankment.jpg
Previously, during the time of Ancient Rome, most of the banks of the Tiber were natural and looked more like this:
At its zenith, Rome was a high functioning metropolis for over a million people. This included a large population of slave labor and the urban poor who were employed as custodial maintenance workers.
The city of Rome also boasted a well engineered sewage system which ensured the city would be protected from the seasonal flooding of the Tiber River.
While the slave population existed, an army of maintenance workers were available to clean up the detritus left by the regular flooding. However, once the Empire fell and the city became a prized target for invading barbarian armies, the vast majority of the population departed the city, both freemen and slave alike, reducing the population to a low of approximately 10,000 people. They were simply unable to maintain the apparatus needed to clean the city.
Post-Empire, each time the city would flood, a layer of sediment and detritus would be deposited on the low lying areas of the city. With no one cleaning it up, each subsequent flood would add to that layer.
Multiply these thin layers of dirt and sand by the multiple floods experienced each year, and multiply that by a few centuries of abandonment that the city went through, and you will soon have many meters of earth covering parts of the city which were exposed during the Empire.
This process also occurred during the republic, before the city was able to develop effective engineering solutions for the flooding.
It is illustrated in the site of basilica di San Clemente, a church from 900ad built atop a church from the 300s which in turn is built atop a Mithraic temple and apartment complex from the first century AD.
One final element that contributed was the repeated barbarian invasions mentioned above- during which times a great amount of vandalism occurred, where many of the municipal functions of the city were purposefully damaged including broken aqueducts and clogged sewers, a few years ago they found a statues head blocking one of the ancient Roman sewers:
