Christianity, especially in its
infancy was quite
vulnerable to those
hostile to its
doctrines. Christians were often
martyred and
persecuted
for their beliefs. Also remember that Christianity began in
Jerusalem, where
Jesus had lived and ministered - if Christians were exaggerating or distorting
the
truth of what had just happened, you can be sure non-Christians would have
immediately pointed those inaccuracies out. But we don't have a record of those
claiming Jesus did not do the things His followers said he did.
The gospels were also incredibly well preserved. There is a large
multiplicity of the manuscripts, and within these manuscripts, there is a high
degree of fidelity. And although there are variants between manuscripts,
these variants are almost entirely inconsequential (ie spelling) and none of
them affect any major Christian doctrines.
Finally, the gospels, like all other books of the Bible, are all markedly
different and yet are consistent with one another. This shows a high
likelihood of independent and authentic observation of the same event.
See also: Are the gospels reliable?