"To begin a relationship" means to start a connection or bond with someone, where you get to know each other, spend time together, and potentially develop feelings for each other. Full definition
This is especially true when beginning a relationship with a trans girl. (freesugardaddywebsite.com)
In Bad Timing, a man and a woman meet and begin a relationship in which neither of them is ever on the same page as the other. (rottentomatoes.com)
Women in the study who began their relationships while on hormonal birth control became less satisfied with the marriage after stopping the medicine, but only if her husband was less attractive than average. (livescience.com)