Potter studied painting with his father Pieter Potter in Enkhuizen. His father was for some time a manufacturer of gilded leather hangings in Amsterdam, but stopped after a few years. Paulus lived at that time in The Hague where he met his wife. He was introduced by her in the Dutch elite. After disagreements with fellow painters and Amalia of Solms-Braunfels, a member of the stadholder's family, he left for Amsterdam. Potter was invited by Nicolaes Tulp, who was impressed by his civilized behavior and politeness. Potter painted his son Dirck Tulp.
In a short time he succeeded in producing about a hundred paintings, working continuously.