Since "Sol Invictus, the Roman sun god" is a mythological figure who never actually existed, he doesn't have an actual "birthday", thus rendering your question somewhat moot.
The most common explanation for why Christmas is when it is is that someone in the early church decided it was better to give people an at least nominally Christian reason to celebrate when their ancestors had been celebrating for hundreds of years than to have them keep honoring some pagan god.
AnswerMithras was a sun god, so his birthday was celebrated on December 25th, the day, shortly after the solstice, when the sun appeared to begin to rise earlier.
The Roman God Neptune is the God of the sea.
Cupid (Roman god of desire) dates from about 800 BC. But the ancient gods were not given dates on the Julian calendar.
There is no Roman god for "worse".
Cult of Mithras the sun God of Rome roman legion god lots of the mythos incorporated into Xtianity Xmas day the same as birthday of Mithras
Mars was a Roman god. He was the God of War.
In Roman mythology, he is the blacksmith god, or the god of the forges.
"ROMAN god" did not discover Jupiter. it is named after roman god...JUpiter
the roman god of is mars so roman god of war means mars
God doesn't have a birthday because he never ages.
the god of light birthday is on 25 December
Pluto was the Roman god of the underworld.