Biblical Calendar - New Month 1 or 2 Days After Dark Moon?

A special question for people who have studied previously the biblical calendar and its relationship with the moon phases. Most of us agree that the New Moon (aka First Sliver / First Crescent / Waxing Crescent) occurs immediately after the Dark Moon, which lasts according to my investigation 21-26 hours. I notice now in the Hebrew calendar that it usually assumes the first day of a month being the day after the Dark Moon, while the Islamic calendar varies from 1 to 2 days after the Dark Moon. I do generally distrust Islam, but wonder if the beginning of a biblical month possibly occurred constantly on day 2 after the Dark Moon, considering also that the Jews nearly lost track of their own calendar after Babylon and not always applied the Bible correctly as we are well aware of. **Option 1 · New Month = Dark Moon +1 day · First Crescent has to be predicted and New Month actually starts hours before the New Moon can be observed.** Dark Moon First Crescent Adar 30 ............. ┃ ............. Abib 1 .............┃ ............. Abib 2 **Option 2 · New Month = Dark Moon +2 days · First Crescent can be observed the night before the New Month starts.** Dark Moon First Crescent Adar 29 ............. ┃ ............. Adar 30 .............┃ ............. Abib 1 Basis for both options is the sunrise-sunrise rhythm of a biblical day (1Sam 19:11). But even if the erroneous sunset-sunset-rhythm would be assumed, the announcement of the New Year would have to occur in all Israel simultaneously and within minutes after the New Moon becomes visible at night (sacrifices for the new month needed to be prepared and the horn was to be blown).