Early Christianity stayed close to its Jewish roots. First and second century Christians celebrated Passover. A sermon by Melito of Sardis, the Bishop of Sardis, has been preserved and shows that Jesus fulfilled the Passover mystery.
This sermon the Peri Pascha (On the Passover) shows that Jesus fulfilled Bible prophecies and was the final sacrifice that brought forgiveness for our sins.
Melito's sermon stated:
For God replaced the lamb, and a man the sheep; but in the man was Christ, who contains all things.
Hence, the sacrifice of the sheep, and the sending of the lamb to slaughter, and the writing of the law–each led to and issued in Christ, for whose sake everything happened in the ancient law, and even more so in the new gospel.
Jerome, the Catholic scribe that translated the Bible into Latin (the Vulgate), preserved some of Melito of Sardis' writings, according to Wikipedia.