How do we know Jesus really performed miracles?

How do we know Jesus actually performed miracles and was the Messiah? I’ve heard a few claims that miracles were common for that time and the people who make this accusation are implying the miracles didn’t happen. The same people said that there were many people claiming to be the Messiah. Is this true?

Baltimore Catechism:

Q. 326. Could not men have been deceived in the miracles of Christ?
A. Men could not have been deceived in the miracles of Christ because they were performed in the most open manner and usually in the presence of great multitudes of people, among whom were many of Christ’s enemies, ever ready to expose any deceit. And if Christ performed no real miracles, how, then, could He have converted the world and have persuaded sinful men to give up what they loved and do the difficult things that the Christian religion imposes?

Q. 327. Could not false accounts of these miracles have been written after the death of Our Lord?
A. False accounts of these miracles could not have been written after the death of Our Lord; for then neither His friends nor His enemies would have believed them without proof. Moreover, the enemies of Christ did not deny the miracles, but tried to explain them by attributing them to the power of the devil or other causes. Again, the Apostles and the Evangelists who wrote the accounts suffered death to testify their belief in the words and works of Our Lord.

There were indeed many claims of miracle workers in the 1st century. However, they usually had few followers and were regularly exposed. Had Jesus not performed miracles in the presence of many then the Gospels would have been rejected by the people who lived in the areas that the Gospels say the miracles took place. The claims of miracles would have been relentlessly mocked and the followers of Jesus would have been “run out of town.”

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