The record that I have shows Mrs. Elizabeth (Smith) Foster's date of birth as 19 Apr 1722, and it shows her five siblings (Gregory, Thomas, Anthony, Martha and Anne) as having been born between 31 Dec 1712 and 24 Dec 1719....so Elizabeth was the youngest. My guess is that these exact dates of birth cab be found in the Christ Church Parish birth records. My record shows that both her father Thomas Smith, as well as her grandfather John Smith, died sometime before 4 Jun 1723 (the date that Thomas' will was proved).
Thomas' wife Anne had her own will proved on 4 Jul 1749, and it mentioned her daughter Elizabeth Foster (among others). Thomas' will, however, did not mention Elizabeth, since it was written on 9 March 1722....i.e., before Elizabeth was born. There is a codicil to Thomas' will, however, that states that his wife was "with child."