No impact on society? An estimated 2+ billion Christians live on Earth now, roughly 1/3 of all people on Earth. The total world population at the time of Jesus was roughly 250,000.
Most of the world's universities, social structures, most magnificent architectural structures are due to Christian influence as is much of the literature, art, and music that has been preserved and has endured into modern times. The Bible has been the world's best selling book pretty much since the Gutenberg Bible was first published.
Most private social agencies, thrift shops, homeless shelters and ministries, ministries to lepers, addicts, orphans, and hands on ministries to some of the world's most poor and desperate people are founded and staffed by Christians. (Pretty much none by Atheists.)
With very few exceptions, almost all of the world's most prosperous nations were heavily influenced by Christian organization, philosophy, and doctrines. That would include the United States.
With very few exceptions, even in countries with little Christian presence, most of the world's calendars and the identification of the centuries are based in part on the agreed birth of Jesus of Nazareth.
Those who do not wish to believe this will of course pick this or that story or fact from the Bible and hold it up as evidence that it is all bunk. Many of those stories are indeed debatable as whether they are based on historical people or events or whether they are symbolic or parable to teach a concept. And it is legitimately debatable whether Jesus was God in human form or whether he was just a man.
But nobody with any intelligence or education is willing to say that Jesus of Nazareth never existed or that he did not have a profound affect on humanity as no other single individual ever has had.