You are thinking of Christmas as a date, which is understandable.
But Pagan Christmas was at a time, a time exactly decided by the first signs of a return of the winter sun. So, about 4 days after mid winter solstice.
And, amazingly, that's when Christians held their feast as well..... a reversal in the old pagan ways, just like Christianity reversed in to places where folks gathered, or what they believed. And that happens to be 25th December.......
I find there is Nothing in 1st-century Christianity ( Bible record ) that says: ' that's when Christians held their feast as well...'
Jesus nor his followers never held such feast or feasting.
Before people became Christians they did such things, and were warned about returning back to such things - Galatians 4:8-11
Jesus' apostles never celebrated Jesus birthday.
The only instruction Jesus gave was to hold a memorial of his anniversary ' day of death ' the Spring month of Nisan, the 14th day - Luke 22:19
With the death of the apostles an apostasy set in, the genuine 'wheat' Christians would be growing together with the fake 'weed/tares' Christians.
Grow together until the Harvest Time or our time frame - Acts of the Apostles 20:29-30; Matthew 13:24-30