My son was born white how long would it take for him to get his true complexion?

No Good Answer: There is no good answer as it varies from patient to patient and their genetics.

Skin complexion: There is no way to predict the future complexion based on the new born's complexion. It is common for babies to have temporary colors like blue motting and temporary peeling of skin that may make the complexion look little different but future complexion is unpredictable and ids based on genetics.

Time will vary: Everybody's genetics are different. The cells that produce your skin pigment respond to many different influences, such as light exposure, temperature, even irritation of the skin/rashes. I've seen some kids who have their complete pigment by their first birthday, and others whose skin tones continue to change even into puberty in response to hormonal output. I bet your child is beautiful!