The index PANEL at the FAMILY tab will automatically give last names first, then by birth date as the secondary sort. Having this panel in your view or not is customizable.

Last name first is the default primary sort, but you can also choose the primary sort of first name, birth, death, or marriage)

However, if you are talking about the POP-UP Index by F-2 or the Main menu > Persons > Index, or the Person Tab - index button in the mini-tree, the index will NOT give you a secondary sort on the birth date. A few will be in birth ordr, then a few out of sequence, the a few in a different sequence, etc.