December 25th was literally just the date of the annunciation + 9 months. Jewish and Christian tradition held that the world was created on March 25, therefore the coming of the new world through Christ in the annunciation to Mary was held to also be March 25th. The December dating had nothing to do with the actual physical dating of things but of internal logic. This is why, for instance, the Orthodox Church doesn't care that their dating of Easter is shifting later in the year over time with respect to actual astronomy. The date of Easter was fixed to be the first Sunday after the first full moon after March 21 on the Julian calendar by the Council of Nicaea, but the Julian calendar is slightly longer than the actual solar year which results in it falling behind by a day every 128 years. That's a self-correcting issue though, because after a long enough time it means Easter (as well as Christmas) will have been celebrated on every single day of the year! This effect isn't present with the Gregorian calendar though, which the Roman Catholic Church instituted in the 1500s to try and bring things back in line with the solar year due to advances in astronomy by Copernicus, Brahe, etc. While that's fine for secular and civil purposes, whether it made the church more credible from a religious point of view is your call. For what it's worth, the calendar included in the publication of the King James Version in 1611 was Julian. When England switched to the Gregorian calendar for civil purposes in 1752, the calendar became obsolete.
If the church actually wanted to use astronomy and astrology to determine the dating of Christ's birth, keep in mind they had access to the works of ancient mathematicians, astronomers, and astrologers. They had access to the works of the people that invented these fields that have long since been lost to modernity. The Egyptian city of Alexandria, aside from being a major centre of Christianity, was also a major centre of ancient astronomical observation. In fact, an Alexandrian had established the Julian calendar and the city was given the honor by the church of spotting the first full moon after March 21st for Easter in recognition of their talents. They went with the calendar of dates established and have stuck with it through the centuries despite the church being divided by politics and turmoil.