Was the date of Christmas just derived from Saturnalia and other winter pagan festivals?

This picture and the answer at https://christianity.stackexchange.com/questions/5144/why-is-christmas-on-december-25th seems to explain the biblical basis of the date. https://www.youtube.com/watch?v=D11jAEKgB2o , the topmost answers however on https://history.stackexchange.com/questions/46227/how-did-christianity-replace-roman-paganism-and-other-ancient-religions and https://christianity.stackexchange.com/questions/44832/is-christmas-not-a-christian-festival speak of adoption of Saturnalia and absorption of Paganism and also how the celebration of Christmas was probably a combination of "probably a combination of pagan solstice holidays, early Catholic church assignment of saints days, and the desire of northern Germanic tribes (for whom winter was much more arduous) to have a celebration for home and hearth." https://christianity.stackexchange.com/questions/69613/could-december-25-as-the-birthday-of-jesus-have-come-from-pagan-influences even talks about how there is no biblical basis for the birthday of Christ to be set on 25th December. This also seems to go against the information in the picture. So is there a basis for Christmas on 25th December just being a rebranding of a Pagan tradition given that there is a biblical basis for it? Or was the biblical scriptures interpreted only much later to cater as reasoning to the 25th December date?