No, Stock Markets in the United States are closed on New Year's Day, Sunday, January 1st, 2023
New Year's Day is a Federal Holiday in The United States. This means that The US Stock Markets are closed on that day. Additionally, the markets will observe New Year's on Monday, January 2, 2023, so that means markets will also be closed that day too. The stock market will reopen on Tuesday, January 3, 2023.
Source 1 - https://www.nyse.com/markets/hours-calendars