Below are quotes from various sources, which tell us what the new moon was in times past.
The new moon began when the thin crescent of the new moon was first visible at sunset. (Theological Wordbook of the Old Testament, vol 1, p. 266)
The ancient [pagan] Greeks recognized the visible new moon as the beginning of the month when they celebrated the “sickle of the new moon” with offerings and meals. This was also the case with the ancient Babylonians who worshipped the new moon as the goddess Isis, and had her wearing a horns, which resembled the new moon.” (TDNT, vol. 4, p. 639.)
The new moon festival maintained its importance in the Jewish cultus up to New Testament times. The time was not set by astronomical calculations but by observation….[Jewish law] demanded that…as many witnesses as possible should report the appearance of the sickle to the appropriate authorities.” (TDNT, vol. 4, p. 640.)
The ancient Jewish calendar depended not on mathematical calculations and arrangements, but was set from month to month according to the physical appearance of the new moon. Witnesses who had seen the first sign of the crescent on the horizon after sunset were expected to report the fact to the authorities, who thereupon published throughout the country the fact that the new month had begun. (The Pharisees, by Louis Finkelstein, p. 601, Jewish Publication Society, 1938, Philadelphia., based on talmudic literature)
Until Hillel II instituted a permanent calendar based on calculations (ca. 360), the fixing of the new moon was determined by observation and the evidence of witnesses. During the earlier period, the practice of adding a second day to festivals … was introduced for communities lying at a distance from Palestine, because it was doubtful on precisely which of the two days the new moon occurred.” (Encyclopedia of the Jewish Religion, p. 78; Massada-P.E.C. Press Ltd, 1965., based on talmudic tradition)
In old Israel the new moon—the day after the crescent was first sighted in the sky—was celebrated by sacrifices and feasting…” (Judaism, by George Foot Moore, professor of the history of religion, Harvard, vol 2, p. 22, based on talmudic literature)
The ancient Jewish calendar depended not on mathematical calculations and arrangements, but was set from month to month according the physical appearance of the new moon. Witnesses who had seen the first sign of the crescent on the horizon after sunset were expected to report the fact to the authorities, who there upon published throughout the country the fact that a new month had begun.” (The Pharisees, pp. 601–602, by Louis Finkelstein, professor of theology at Jewish Theological Seminary of America; Jewish Publication Society of America, 1938., based on talmudic literature)
~ “The phases of the moon could easily be recognized by everybody. The new moon indicated the beginning of the month.… Though the ‘new moon’ could be observed by every individual, to prevent any mistake or doubt the duty of fixing the new month was assigned to a rabbinical council in Jerusalem. Their decision was subject to the testimony of two reliable witnesses. As soon as their reports have been received and checked by astronomical calculation, an official message was sent out by chains of fire signals” (The Judaic Heritage, by Rabbi Dr. R. Brasch, pp. 22, 24, based on talmudic literature)
“Rosh Chodesh [is the] Hebrew term meaning ‘the beginning of a month’ applied to the religious half-holiday observed in connection with the appearance of the New Moon; that is, the beginning of each new month of the Hebrew calendar.” (The New Jewish Encyclopedia, p. 409, Behrman House Publishers, 1976, based on talmudic literature)
Specific Quotes from Talmud:
“The Sanhedrin was assembled in the courtyard (“bet ya’azek”) of Jerusalem on the 30th of each month from morning to evening, waiting for the reports of those appointed to observe the new moon; and after the examination of these reports the president of the Sanhedrin, in the presence of at least three members, called out: “The New Moon is consecrated”; whereupon the whole assembly of people twice repeated the words: “It is consecrated” (R. H. ii. 5-7; Sanh. 102)
“In the times of the Second Temple it appears from the Mishnah (R. H. i. 7) that the priests had a court to which witnesses came and reported. This function was afterward taken over by the civil court (see B. Zuckermann, “Materialien zur Entwicklung der Altjüdischen Zeitrechnung im Talmud, “Breslau, 1882). The fixing of the lengths of the months and the intercalation of months was the prerogative of the Sanhedrin, at whose head there was a patriarch or THÑb. The entire Sanhedrin was not called upon to act in this matter, the decision being left to a special court of three. The Sanhedrin met on the 29th of each month to await the report of the witnesses.”
The new moon was reckoned by actual personal observation, not by astronomical calculation….So important was it deemed to have faithful witnesses, that they were even allowed, in order to reach Jerusalem in time, to travel on the Sabbath, and, if necessary, to make use of horse or mule (Mishnah Rosh ha Shana, i. 9; iii 2). While strict rules determined who were not to be admitted as witnesses (Mishnah Rosh ha Shana, i. 8), every encouragement was given to trustworthy persons, and the Sanhedrin provided for them a banquet in a large building specially destined for that purpose and known as the Beth Yaazek (Mishnah Rosh ha Shana, ii. 5).
In the Mishnah, the book containing the late second century record of Jewish legal rulings and other religious records, we find recorded that the Jews’ religious leaders established rigorous protocols and rituals for determining when the new moon had been sighted. The following quotes are from the Mishanah.
“A father and son who saw the new moon…” (Rosh Hash 1:1a) “Tobiah, the physician, saw the new moon in Jerusalem…” (Rosh Hash 1:7e) “He who saw the new moon…” (Rosh Hash 1:9a)
The Mishnah then goes on to discuss how to examine those who claimed to have been eye witnesses of the new moon to determine if their testimony was accurate or not (Rosh Hash 2:6ff). One of the questions the religious leaders in Jerusalem would ask of the Jewish witnesses was, “How did you see the moon?” (Rosh. Hash 2:6c). The Jewish leader, Gamaliel [of Acts 5:34] actually showed pictures of the shapes of the moon to the witnesses to help ascertain the accuracy of the witnesses’ testimony (Rosh Hash 2:8).
Philo of Alexandria was a prominent Jew that lived from approximately 20 BC to 50 AD. So not only did he live before the Messiah, he lived during and after as well. We know that Philo’s writings and beliefs are consistent with the Jews beliefs because he was hand picked by the Jews of that time to head a Jewish delegation to represent the Jews in a massacre that had occurred against the Jews in 39 AD. We know that Sabbath observance is a staple in Jewish belief. The Jews would not have selected someone to represent them had that person not kept the correct day for the Sabbath.
“For it is said in the Scripture: On the tenth day of this month let each of them take a sheep according to his house; in order that from the tenth, there may be consecrated to the tenth, that is to Elohim, the sacrifices which have been preserved in the soul, which is illuminated in two portions out of the three, until it is entirely changed in every part, and becomes a heavenly brilliancy like a full moon, at the height of its increase at the end of the second week”.
“And this feast is begun on the fifteenth day of the month, in the middle of the month, on the day on which the moon is full of light, in consequence on the providence of Elohim taking care that there shall be no darkness on that day.”
“…there is one principle of reason by which the moon waxes and wanes in equal intervals, both as it increases and diminishes in illumination; the seven lambs because it receives the perfect shapes in periods of seven days—the half-moon in the first seven day period after its conjunction with the sun, full moon in the second; and when it makes its return again, the first is to half-moon, then it ceases at its conjunction with the sun.” [All emphasis supplied by author/complier of this study.]
“First of all, it is the beginning of the month, and the beginning, whether of number or of time, is honorable.
Second, because there is nothing in the whole heaven destitute of light. (141)
Thirdly, because at that period the more powerful and important body gives a portion of necessary assistance to the less important and weaker body; for at the time of the new moon, THE SUN BEGINS TO ILLUMINATE THE MOON WITH A LIGHT WHICH IS VISIBLE to the outward senses, and then she displays her own beauty to the beholders. And this, as it seems, an evident lesson of kindness and humanity to men, to teach them that they should never grudge to impart their own good things to others, but, imitating the heavenly bodies, should drive envy away and banish it from the soul” (page 581).
Clement lived between 150 AD and 215 AD. So well into the 2nd century, the lunar Sabbath was still kept.
“in periods of seven days the moon undergoes its changes. In the first week she becomes half moon; in the second [week], full moon; and in the third [week], in her wane, again half moon; and in the fourth [week] she disappears.”
“The beginnings of the months were determined by DIRECT OBSERVATION OF THE NEW MOON. Then those beginnings of the months (Rosh Hodesh) were sanctified and announced by the Sanhedrin, the Supreme Court in Jerusalem, after WITNESSES had testified that they had SEEN THE NEW CRESCENT and after their testimony had been thoroughly examined, confirmed by calculation, and duly accepted” (p.1).