Bernd 11/22/2022 (Tue) 06:34 No.49248 del
It's hard to say because a lot of these kinds of things could easily convergently evolve. There are end of year/midwinter celebrations in most cultures that exist or have existed.

Saint Nicholas was a saint known for giving three girls money so their father could get them married and they could avoid a life of poverty, he did not want it known that he gave these gifts so he threw a purse of money through the window of their house during the night and then repeated this on two more nights until each daughter could be married.
The Feast day of Saint Nicholas is the 6th of December and on that day to celebrate him it was customary to give children gifts but then the reformation hit.

>During the Middle Ages, often on the evening before his name day of 6 December, children were bestowed gifts in his honour. This date was earlier than the original day of gifts for the children, which moved in the course of the Reformation and its opposition to the veneration of saints in many countries on 24 and 25 December. The custom of gifting to children at Christmas was propagated by Martin Luther as an alternative to the previous very popular gift custom on St. Nicholas, to focus the interest of the children to Christ instead of the veneration of saints. Martin Luther first suggested the Christkind as the bringer of gifts. But Nicholas remained popular as gifts bearer for the people.

>Father Christmas dates back as far as 16th century in England during the reign of Henry VIII, when he was pictured as a large man in green or scarlet robes lined with fur.[15] He typified the spirit of good cheer at Christmas, bringing peace, joy, good food and wine and revelry.[15] As England no longer kept the feast day of Saint Nicholas on 6 December, the Father Christmas celebration was moved to 25 December to coincide with Christmas Day.[15] The Victorian revival of Christmas included Father Christmas as the emblem of good cheer.[16] His physical appearance was variable,[17] with one image being John Leech's illustration of the "Ghost of Christmas Present" in Charles Dickens's festive story A Christmas Carol (1843), as a great genial man in a green coat lined with fur who takes Scrooge through the bustling streets of London on the current Christmas morning, sprinkling the essence of Christmas onto the happy populace.

Many people, including Wikipedia attribute Odin as being the origin but I think there is just too much of a gap in time between the worship of Odin and the creation of Father Christmas and as you mention we also have a gap in early Christianity where Christmas wasn't celebrated, I am not saying it's impossible but I think it's far from certain.

Pine Trees, stockings, reindeer and such are to be expected. As it's a winter celebration people are going to pick wintery themes to associated with it. Most of England does not even receive snow on Christmas, a white Christmas is rare in England, but people like the cozyness of winter for the celebration so they create and spread wintery ascetics for the celebration, it's why Santa Claus comes from the north pole and not Anatolia. And naturally people are going to pick wintery things to go with a wintery celebration, such as pines as they are ever greens, reindeers which are from snowy lands and big fur lined jackets which radiate warmth and cozyness.
Much of these traditions build on themselves until we reach a point where they are fairly well established and set in stone, like for example my above quote mentions Father Christmas wearing green, that never happens now, it would be heresy.