Like the broader financial markets, the most volatile and active period of the US30 index is in the first two hours of the trading session.
This means that from 9:30 a.m. to 11:30 a.m. generally have the most volumes.
When the best time to trade might depend on the type of investor you are and perhaps what direction the index is traveling.
If you are a day trader, you would typically want to trade in this period. However, if you are the typical investor, you want to buy at specific price points you have listed in your investment strategy or when there are immense dips.