Final answer:
The two special days when catechumens were typically received into the early Church were Pentecost and the Meeting of the Lord in the Temple. Pentecost occurs fifty days after Easter, and the Meeting of the Lord is celebrated on February 2.
Step-by-step explanation:
The two special days out of the year when catechumens would be received into the Church in the period of the early Church were Pentecost and the Meeting of the Lord in the Temple. Pentecost commemorates the descent of the Holy Spirit upon the Apostles and happened fifty days after Pascha (Easter). It was a time marked for the initiation of new members into the Christian faith. The Meeting of the Lord in the Temple is observed on February 2 and recalls Mary and Joseph's presentation of Jesus at the Temple, as well as His recognition as the Messiah by Simeon and Anna. This day also became an occasion for catechumens to join the faith, emphasizing the unity of the Old and New Testaments through the fulfillment of prophecy with the coming of Christ. These occasions were vital in aligning the rhythm of church life with significant events that defined early Christian identity and teachings.