David Marcus (Merritt Butrick) was introduced in the second Star Trek: The Original Series movie, Star Trek II: The Wrath of Khan, but the question of when Admiral James T. Kirk (William Shatner) and Dr. Carol Marcus (Bibi Besch) had a son who was an adult by 2285 could be answered by Star Trek: Strange New Worlds. David and Carol were the masterminds of Project Genesis, technology that could terraform dead worlds for the United Federation of Planets. Khan Noonien Singh (Ricardo Montalbán) stole the Genesis Device as part of his revenge plot against Admiral Kirk and the Federation, but the technology also had a dark secret thanks to David Marcus.
https://screenrant.com/star-trek-kirk-son-david-marcus-when-born/