Baldwin was born and grew up in Madison, Wisconsin. Her mother, who died in 2017, was 19 and going through a divorce when Baldwin was born. Baldwin was raised by her grandparents and spent Saturdays with her mother, who suffered from mental illness and opioid addiction. Her maternal grandfather, biochemist David E. Green, was Jewish (the son of immigrants from Russia and Germany), and her maternal grandmother, who was Anglican, was English-born. Baldwin's aunt is biochemist Rowena Green Matthews. Through her maternal grandfather, Baldwin is a third cousin of comedian Andy Samberg.