December 25th was not celebrated as the birthdate of Jesus Christ until the year: 240 AD, 300 AD, 400 AD, or 440 AD?

I wonder if there's a definitive answer to this ... two of these say 336, one says 333, and another says 354:-

Christmas (i.e., the Mass of Christ) was not among the earliest festivals of the church. According to a Roman almanac, the Christian festival of Christmas was first celebrated in Rome on December 25th in AD 336. Prior to this, throughout the Roman World, the Saturnalia from 17th December was a time of merrymaking and the exchange of gifts.
http://messianicjudaism.homestead.com/christmas.html

he birthday of YAHSHUA (Jesus) was never observed by the apostles or the early Messianic Faithers. His birthday was first celebrated by the Roman Catholic Church in 333 AD.
domaintrader2000.com/dov-xmas.htm [no longer exists]

By the year 273, most leaders settled on December 25 as the natal day, most likely because two other festivals were already being celebrated that day ... Christmas was first celebrated on December 25 in 336, after Emperor Constantine had declared Christianity the Roman empire's favored religion. For a while, Eastern churches, however, celebrated January 6 as the date for the birth of Jesus and his baptism. Most Eastern Orthodox churches eventually adopted December 25, celebrating the birth on the earlier date and his baptism on the latter, but the Armenian church still celebrates his birth on January 6.
newcelebrations.com/newsletter_5.htm [no longer exists]
https://www.biblicalarchaeology.org/daily/people-cultures-in-the-bible/jesus-historical-jesus/how-december-25-became-christmas/

We are nowhere told that Christ was born exactly at the time when the 'star' appeared; but it is safe to say that His birth took place some time between the middle of A.U.C. 747 and the end of A.U.C. 749, i.e. 7 BC and 5 BC. The previously mentioned March 25th day was the pagan festival of spring. The church adopted this date as that of Mary's visits by the angel Gabriel, and added nine months to it to come of with December 25th as the day of Jesus' birth. Christ Mass, later called Christmas was first celebrated in the year 354, December 25th, according to several sources.
att.virtualclassroom.org/vc99/vc_41/singa/christmas/xmasorigins.html [no longer exists]

December 25 is the Roman festival called Sol Invictus the birth of the sun (days becoming longer). The Mithraists celebrated a mithraic love feastin this day. This feast consisted of loaves of bread decorated with crosses with wine over which the priest pronounced a mystic formula. According to Collier Encyclopedia after the triumph of Constantine the Church at Rome assigned the 25 December as a day of celebration and feast about 320 or 353 AD.
toolong.com/christmas.htm [no longer exists]