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A new moon was recognized at the first sliver of the waxing crescent (see discussion by Ben Dreyfus here). This was done by the Jews by observation until the 4th century, and by calculation thereafter (source).
Because a true lunar month is approx. 29.5 days, an observed lunar month would last either 29 or 30 days. That the beginning of the month was determined by observation in Biblical times did not mean they didn't know when the new moon would be--they could always narrow it down to one of two possible dates (+29 or +30 from the last new moon). So it's not at all unrealistic that people would know the new moon was coming the next day (such as Jonathan in 1 Samuel 20:18).
In fairness to the ancient astronomers, they spent a lot more time looking at the heavens than most of us do, so while error is possible in an observed system, I suggest we give them the benefit of the doubt (in the absence of conflicting evidence) that they knew what they were doing--they saw a waxing crescent (though not quite as quickly as it could have been seen with a telescope) and validated the beginning of a new month. Waiting until dark moon +2 days would generally have been unnecessary.
As noted in the link above to Dreyfus' work, for a time the Jews used signal flares to rapidly transmit--over long distances--the news that a new month had been recognized.
Whether we're counting days from sunrise to sunrise or from sunset to sunset wouldn't make a significant difference to this specific question--the new month began when a sliver of the waxing crescent could be seen & validated--this could be within a few hours of the dark moon.
Upvote:1
It's possible that this question is moot.
Consider:
… This day [Feast of Tabernacles] is holy unto the LORD …
— Nehemiah 8:9
Thou shalt keep the feast of unleavened bread: (thou shalt eat unleavened bread seven days, as I commanded thee, in the time appointed of the month Abib …
— Exodus 23:15Blow up the trumpet in the new moon, in the time appointed, on our solemn feast day.
— Psalm 81:3
The secret things belong unto the LORD our God: but those things which are revealed belong unto us and to our children for ever …
— Deut. 29:29
There shall not be found among you … an observer of times …
— Deut. 18:10Ye shall not … observe times.
— Leviticus 19:26For these nations, which thou shalt possess, hearkened unto observers of times, and unto diviners: but as for thee, the LORD thy God hath not suffered thee so to do.
— Deut. 18:14
If God had defined which days are holy to him, and had appointed the specific times when they occur, would he have then left it to chance, allowing human observers (which can be unreliable, or impossible due to weather) to choose each day? And if he had expected observation to decide which day begins each month, why would he have then forbidden observing times?
Doesn't it make more sense that God had taught Moses how to calculate the holy calendar (just as the Jews still do in our current time), and that this calculation has been passed down and preserved for 3500 years?
Much of the above is based on The Crucifixion Was Not On Friday — Herman L. Hoeh — 1968