I Want To Hold Your Hand was the Beatles’ first American hit. The song was number 1 for the entire month of February and the first 3 weeks of March, 1964.
However, it was on February 22, 1963 that the Beatles charted their first number 1 song in the United Kingdom. They formed their Northern Songs publishing company the same day.
That song had been recorded in late 1962 and would peak at number 3 on the US charts in March 1964.
Here are the Beatles performing Please Please Me on the Ed Sullivan show: