Colostrum Is Breast Milk
No, your milk didn't "come in" on day 3, you had milk from the moment your baby was born.
Colostrum is the first type of breast milk that is characterized by a yellow color and sticky texture. One of the main reasons for the colostrum in the early days is to coat your baby’s gastrointestinal tract to keep harmful pathogens from latching on. It is not an accident or evolutionary error that colostrum is produced in small amounts - the lower volume helps newborns learn how to coordinate sucking, swallowing, and breathing safely. Colostrum has higher quantities of immune factors to keep your baby healthy and protect their immature immune systems.
Colostrum has all that your baby needs to gain and grow in the first days of life. Usually after around 48-72 hours after giving birth, your milk supply will significantly increase and change its makeup to adapt to the needs of your growing baby. There is no need to supplement unless a parent is not able to or chooses not to breastfeed, or there is a medical need for supplementation (ex. not enough wet and dirty diapers, jaundice that is not improving with breastfeeding, etc.). It is normal and expected for a baby to lose up to 7% of their birth weight, and potentially more in the case of a c-section or use of significant amounts of IV fluids during labor.
When providers use phrases like "milk coming in after birth", it makes parents feel like they are doing harm to their babies if they do not supplement. Parents need to know that colostrum is breast milk and what happens 2-4 days after birth is a significant change in milk volume and makeup, but NOT the arrival of milk itself.