Israel's birthday is May 14, 1948 because that's the day it was declared a country.
Birthdays were not customarily recognized or celebrated in the Old Testament so Jacob/Israel's birthday is unknown. If you are referring to the modern Nation-state of Israel, then it was declared 14 May 1948 and recognized by the U.N. on 15 May 1948.
Elizabeth Israel was born on January 27, 1875.
Steve Israel was born on May 30, 1958.
Israel Kamakawiwo'ole was born on May 20, 1959.
Israel Putnam was born on January 7, 1718.
Israel Asper was born on August 11, 1932.
Israel Gelfand was born on September 2, 1913.
Israel Vasquez was born on December 25, 1977.
Märt Israel was born on September 23, 1983.
Israel Folau was born on April 3, 1989.
Israel Dagg was born on June 6, 1988.