During the time that the Sanhedrin existed, witnesses had to come to the Sandhedrin and testify to their viewing of the "new" moon. The Sanhedrin would sanctify the month after confirming their testimony. (On some occasions, Sanhedrin would declare it automatically without witnesses.)
Prior to the Sanhedrin, before kings existed, during the days of the Judges, did they use witnesses, and who made the final decision to declare Rosh Hodesh?
I'm inferring that the Sanhedrin as well as those who were in charge knew the exact time of the molad. During the time that Sanhedrin existed in Jerusalem, and later in Yavneh, etc., they waited for witnesses to appear, and thus, there were times when there were 2 days of Rosh Hodesh because of doubt of the length of the month. I'm inferring that if they didn't use witnesses and relied on the declaration of the Sanhedrin, there would be no doubts.
I will ask, separately, regarding how the message was sent to far away places.