Er, saying the birth date of Jesus is off by a few years isn’t the same as saying he didn’t exist at all.
Our AD system of years was devised in the 6th century by a dude Dionysius Exiguus who probably wanted to replace an existing dating system based on the reign of Diocletian, the Era of Martyrs.
But no one really knows how Dionysius worked it out exactly, or if he even actually used the birth date and not some other shit like nativity. The bible itself doesn’t give exact dates, people commonly dated it by a passage saying he was about 30 during the 15th year of the reign of Tiberius, so you have to work out how long ago Tiberius’ reign was and then go from there, but it also doesn’t say he was exactly 30…
Then there’s other shit like how the diocletian era system had a different start date and some confusion over exact ruling lengths of emperors which would mess up counting back through the years.
So this, coupled with scholars trying to figure out dates of things in the bible based on trying to date events mentioned like the census has led to biblical scholars dating the birth to like 4 or 5 BC and that the dude who was trying to figure that out 600 years after the event got it a bit wrong.
It’s wiki so not the greatest source, but this article goes over most the issues about trying to date the birth
Dating ancient events can be tricky when people were using different dating systems based on shit like when roman consuls or emperors reigned, or when the Olympics happened, or from years since the biblical creation (anno mundi, still used in the Hebrew calendar for religious purposes).
Adoption of the AD system of counting years by most of Europe by the 10th century has made dating since then a lot easier. But even then you have some annoyances like the adoption of the Gregorian calendar which not everyone did at the same time or in the same way leading to differences of up to 2 weeks between the different systems: like how the Russian February Revolution of 1917 actually took place in March because the Russians refused to adopt the Gregorian calendar until after they overthrew the tsar, and a bunch of Orthodox Christians still use the Julian calendar for the dates of religious holidays like Christmas.
So to end this long rambling diatribe: dating old shit ain’t an exact science and dates of ancient events can be a bit blurry.