... I had a friend who is a Muslim told me that Jesus' birth and crucifixion was a made up.
Does he mean that Jesus never existed? If so, then he's not a very knowledgable Muslim.
Muslims believe that Jesus existed. However, they do not believe that he was crucified or that he is God incarnate.
In Islam, Jesus (Arabic: عيسى `Īsā) is considered a messenger of God who had been sent to guide the Children of Israel (banī isrā'īl) with a new scripture, the Injīl (gospel). The Qur'an states that Jesus was born to Mary (Arabic: Maryam) as the result of virginal conception, a miraculous event which occurred by the decree of God (Arabic: Allah). To aid him in his quest, Jesus was given the ability to perform miracles, all by the permission of God. According to Islamic texts, Jesus was neither killed nor crucified, but rather he was raised alive up to heaven.
Like all prophets in Islam, Jesus is considered to have been a Muslim, as he preached for people to adopt the straight path in submission to God's will. Islamic texts forbid the association of partners with God (shirk), emphasizing the notion of God's divine oneness (tawhīd). Jesus is seen in Islam as a precursor to Muhammad, and is believed by Muslims to have foretold the latter's coming.
How come there are no evidence of Jesus' Crucifixion and birth? Well except Pliny the younger's writings about 1st century Christians.
There are a few historical references about his crucifixion, but they are very few:
From Jewish sources:
- Talmud, b. Sanhedrin 43a: On the eve of the Passover Yeshu [Jesus] was hanged [or crucified]. ... Since nothing was brought forward in his favor he was hanged on the eve of the Passover.
- The Amoa "Ulla" (Ulla was a disciple of Youchanan and lived in Palestine at the end of the third century) adds: "And do you suppose that for (Yeshu of Nazareth - Jesus) there was any right of appeal? He was a beguiler, and the Merciful One hath said: "Thou shalt not spare neither shalt thou conceal him." It is otherwise with Yeshu, for He was near to the civil authority.
From Roman sources:
- Cornelius Tacitus in his Annals, xv. 44: Christus ... was executed at the hands of the procurator Pontius Pilate.
- Lucian of Samosata: (Christ was) the man who was crucified in Palestine
Jesus is famous today, but remember that during his time, he was actually a nobody. In fact, the whole Jewish race were a bunch of nobodies in the Roman Empire.
On the contrary, if you find a lot of historical records about Jesus today, the authenticity of those records would be highly suspicious.