When does constipation in early pregnancy begin?

Anytime! Given that there are plenty of people who get constipated without being pregnant, it can happen anytime, although the rate increases as pregnancy progresses due to the fetus taking up space in the belly. In one study, about 2/3 of pregnant women got constipated at some point. Drinking lots of water and eating a healthy high-fiber diet help a lot; if symptoms continue, please see your doctor.
When / if it does. No set time. Depends on your diet and your underlying regularity. Drink plenty of fluid and consume 5 or more portions a day of fruits and vegetables.