It's doable for a competitor. AIS has the vessels depth. If you assume the weight of a container to be similar you can monitor the vessels depth as they discharge and then load containers. You'll have to account for bunkering, empty containers, etc. Still, it's doable.
There's also some data (not sure if public, should be easy for any shipping company) for anything going to the US. You can use that data to further improve the previous estimates. See https://www.joc.com/regulation-policy/trade-data/united-stat.... Interestingly the JOC is terrible at predicting future trends despite having one of the most detailed data on their trade.
Note: the method above will not give you exact numbers. It's not actually needed to know the exact numbers, seeing the trends and the fluctuations/changes is already quite useful.