At what point did we start measuring time?

The first 'people' based on the cycles of the sun/moon and the rising or animals each day.

If you mean history...that would be when events were first recorded.

The BC scale wasn't proposed until far into the AD era, being that BC refers to the beginning of time up until AD 1.

The AD system was thought up by a Scythian Monk named Dionysius Exiguus in Rome in 525. It was actually a result of a failed calculation to determine the day of Easter. Byzantine chroniclers, such as Theophanes, pursued the idea of numbering each day in their chronicles but differently just for the Judeo-Christian era. An African chronicler named 'Victor' first used AD as his main dating mechanism in the seventh century. Some generations later, an Anglo-Saxon monk named 'Bede', who knew of the work of Dionysius Exiguus, used the Anno Domini dating system as well. AD would also soon be the dominant time measuring scale for Europe, by Charlemagne and his successors.