Not exclusively, but Enumeration at Birth is pushed hard and I saw a stat that I believe said 99% of infants were enumerated at birth (it may have said that 99% of enumerated infants were enumerated at birth, however). This process began in 1987.
Since you need a SSN for a child to get the tax benefits of a child (as of 1986), and most parents will want those, it's an easy sell to get a SSN while processing the rest of the birth paperwork, rather than doing it later. I was born before 1986 and I believe my parents applied for SSNs for me and my siblings around then because it was needed for tax purposes.
They were not originally, but now they are. There is an interesting case of a Texas woman who was born "off-radar" to libertarian parents and had no government documentation of her existence. This caused major problems with access to services and employment in her adult life until a senator intervened and introduced legislation for the situation.
SSNs are not universal, either. There are some unions and religious groups that have legal exemptions.
>SSNs are not universal, either. There are some unions and religious groups that have legal exemptions.
Exempt from participating in social security (the program), not exempt from having a social security number. In fact, getting a social security number is the first step in applying for an exception from social security. Basically, SSA needs to track you as being exempt from social security, which requires a unique identifier.