If you are all living together in the same household you only need to make a decision on who claims the child on their tax return. The one claiming the child will probably be eligible for Head of Household status. The one not claiming the child must file as Single, if not married, and does not enter the child on their tax return.
Whomever claims the child needs to indicate on their tax return that the child lived with them for the Whole year since the child was born in 2019.
