People had been able to calculate and predict the dates of the solstices and equinoxes (and exciting stuff like solar and lunar eclipses) for millennia - see various megalithic structures including Newgrange (older than the pyramids).
Christmas etc were all dated a bit later than the solstices, not on them.
Egyptian Christians believed in the importance of recognising anniversaries. in the early 2nd century they knew Jesus was born in midwinter and suggested dates between 20th December and 4th January before eventually doing a series of calculations based on these Biblical events:
Zacharius was working in the Temple when he heard that his elderly wife Elizabeth was pregnant
Angel Gabriel announced to Mary that she was pregnant
Mary set off on a long and difficult journey to visit Elizabeth (her kinswoman) and, after they greeted each other, Elizabeth's baby (John) jumped in the womb.
Knowledge of the likely date of Zacharius' Temple service suggested:
The Angel visited Mary on March 25th (Lady Day)
John was born on 24th June
Jesus was born on 25th December
Those dates were set by the end on the 2nd century. They do not coincide exactly either with the solstices or with any Roman pagan festivals.
Easter does sometimes coincide exactly with Passover, but not always, partly because of (can't remember the exact date) an early medieval western Christian streamlining decision to fix a notional date of the vernal equinox on 21st March.