This question is answered in detail in an article at this web site, The
Miracles of Jesus. Let us give a synapsis.

The reason for belief in the miracles of Jesus can be separated into two
categories, which are;

1. The reliability of the gospel witnesses.

2. The testimony of non-Christian authors.

The first point is that the gospels have every sign of being a reliable
account of actual events. Most of those who publicly proclaimed the
miracles of Jesus, and most particularly Peter, Mark, and Matthew, to name
a few, were martyred for their faith in Jesus. No one has ever given a
single believable piece of evidence that any of these eye-witnesses were
anything other than truthful and accurate. And not a single one of them
ever relented and backed down on their claims, even upon pain of death.
Perhaps it is possible that a few men and women could have cooked up some
deceitful bogus claims about the miracles of Jesus, although this is very
difficult to believe, given the well-known character of these men and
women. However it is simply not credible that every single one of these
conspirators would have refused to relent, even though their lives were at
stake. Can anyone imagine Peter, after having made up a bunch of miracles
to support belief in a fake Messiah being willing to die for such a lie?
Could every single witness hold up in such a situation. This is not
believable. The miracles as recorded in the Bible are very real indeed.

In addition the the public claims of the apostles and other witnesses that
Jesus worked great marvels, wonders and signs (Acts 2:22), a number of
historians who definitely were not followers of Jesus reported the same
sorts of things, although they did not combine them with faith.

As an example of a non-Christian author who referred to the miracles of
Jesus, consider Flavius Josephus. Josephus was a Pharisee, as well as a
commander of the Jewish forces whose rebellion ultimately resulted in the
destruction of Jerusalem in 70 AD. Josephus wrote about Jewish history for
a largely Roman audience. In his history of the Jews,[1] one can find the
passage:

Now there was about this time Jesus, a wise man, if it be lawful to call
him a man, for he was a doer of wonderful works, a teacher of such men as
receive the truth with pleasure. He drew over to him both many of the
Jews, and many of the Gentiles.

Josephus reports that Jesus was a “doer of wonderful works,” an obvious
reference to his miracles. Josephus was born in 37 or 38 AD. He published
his Antiquities in 93 or 94 AD. As a Pharisee, he surely knew many who
were eye witnesses to some of the events which are recorded in the gospels.

Josephus had an ambivalent attitude toward Christians. It is at least as
interesting to look at some of the writings of the Jewish leaders who were
vehemently opposed both to Jesus Christ and to the movement which he
began. For example, a very interesting passage can be found in the Talmud.
The Talmud is a set of rabbinical teachings and commentaries to the Old
Testament produced in the first and second century AD. In one section of
the Talmud, known as the Baraila one can find the following comment about
the person Jesus:

On the eve of the Passover they hanged Yeshu and the herald went before
him for forty days saying (Yeshu) is going forth to be stoned in that he
hath practiced sorcery and beguiled and led astray Israel. (Babylonia
Sanhedrin 43a)

The author continues on to relate how Jesus was ultimately hanged
(crucified). What is interesting is that in this passage it is stated that
Jesus practiced sorcery. In other words, the Jewish leaders were not able
to refute the well-established fact that Jesus worked many wonders, they
simply accused him of doing them by the power of the devil.

Between the reliable witnesses and the testimony, even of those who did
not accept his claims, one can conclude that Jesus was indeed a worker of
miracles, wonders and signs.

[1]Flavius Josephus, Antiquities, book xviii. chapter iii, verse 3. The
reader should note that the history of this passage is not without
controversy.