Pretty much, there is no record of the exact date from the texts or the letters of the early believers or in the non-canonical writings to my knowledge. There are a significant amounts of writings and references by early leaders like Irenaeus etc. but not on that. Easter can be tied to the Jewish lunar and known historical dates and our calendar is based off the calculations made 6 centuries after the fact and based on recent archaeological evidence year 0 (actual year of birth, isn't actually a 0 AD) is probably around 4 BC.
People are social creations, just look at March 17th and you can see a person from China or India or Egypt etc. wearing green and drinking green beer and knowing nothing of the man Magonus Sochet, his life and teachings. The idea that people felt left out and wanted to celebrate something, but not the pagan celebration, is often credited with the date being chosen. With all the lock downs and government threats and warnings people still get together, go to restaurants even in the Wuhan Pneumonia times.
Looking at history there is just so much ignorance and deliberate delusions and exploitation and abuses of power but that is a long thread onto it's own. The impact of Yeshua (Isa, Ishua, Yesus, Jesus..) teaching is such that even Mahatma Gandhi recognized the impact of Christianity in that his peaceful protests would never have worked against an unChristianized population. Any other group and they likely would have been just cut down and tossed in a hole since to many the value of a life is in its usefulness not in the person themselves.
W.E.H. Lecky (Historian)
"The character of Jesus has not only been the highest pattern of virtue, but the strongest incentive in its practice, and has exerted so deep an influence, that it may be truly said that the simple record of three years of active life has done more to regenerate and to soften mankind than all the disquisitions of philosophers and all the exhortations of moralists."
The study of history and truth takes time and looking, Lee Strobel, Malcolm Muggridge, Josh McDowell, Alister McGrath... all writers that have looked and written on history.
P.S.
Merry Xmas
https://www.ligonier.org/learn/artic...-in-christmas?
http://www.jesuswalk.com/christian-symbols/chi-rho.htm