The problems are that none of the gospels or epistles were written in Jesus' lifetime, and particularly the gospels, they were written anonymously and decades later, so it is not possible if any of the real authors to these gospels were first-handed eyewitnesses. The names that are attributed to 4 gospels were only known in 2nd century CE.
The earliest writings that predated the gospels, were letters of Paul to churches in Greece, Macedonia and Asia Minor, and Paul admitted that he was never around Jesus' ministry in Galilee and Judaea.
Let take the two birth stories of Jesus in 2 gospels, as example.
They have nothing in common, except that Jesus was Mary's son and that he was born in Bethlehem. The rest are inventions by the so-called authors, Matthew and Luke. The details are so different, and that also include the 2 genealogies.
Although both (gospels) say that Jesus was born in the the time of Herod the Great, Luke's gospel added that the birth occurred at the time of census in Judaea, managed by Quirinius, the governor of Syria. But this census didn't occur until 10 years after Herod's death, when Archelaus was banished from Judaea, and Judaea became a Roman province, in 6 CE. Furthermore, Quirinius wasn't governor (legatus) of Syria until 6 CE, and not when Herod was still alive.
If the author (supposedly Luke) can't keep his inaccurate timeline in check, then how are we to trust anything that he had written? Who were Mathew and Luke's sources about Jesus' birth?