What's the earliest you can take your newborn out in public?

Depends: Newborns get a lot of maternal antibody during pregnancy & are protected against many illnesses for weeks. Yet they also are born from a genital area that can pass deadly germs to baby that shows up weeks later. As a rule, any baby with fever>101 <8wks will likely be hospitalized in case what might be a simple fever could be one of the deadly germs. Limited excursions could avoid hospitalizations.

I don't recommend...: ...Taking them out in public until older than 6 weeks. A fever in a child younger than that age is an automatic hospital admission, with a lot of (painful) testing and IV antibiotics until a life threatening illness has either been found or ruled out. Not worth the risk. Stay in situations where you are in control of who is in contact with your baby, like your own or your family's homes.