Christians always worshipped on the first day (Sunday), They called the first day (Sunday) the Lord's day .

Sunday is Sun+day , literally meaning "sun's day"

The official sun god of the later Roman Empire was "Sol Invictus" "Birthday of Sol Invictus" was December 25th.

The Christians celebrate the same day as birthday of Jesus (who is considered as God) even we find in Bible ' And there were shepherds living out in the fields nearby, keeping watch over their flocks at night. 9 An angel of the Lord appeared to them, and the glory of the Lord shone around them, and they were terrified. 10 But the angel said to them, “Do not be afraid. I bring you good news that will cause great joy for all the people. 11 Today in the town of David a Savior has been born to you; he is the Messiah, the Lord'' Luke 2:8

25th Dec it s not time of grazing sheep

and they celebrate the Sunday as Christian's day