You asked about Early Christians. The followers of Jesus before Jesus died were considered disciples.
The disciples were still under the Old Law.
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Yes, the disciples as well as Jesus lived under the old covenant till Christ returned and He blew on them…
“Peace be with you.” 20 When he had said this, he showed them his hands and his side. Then ithe disciples were glad when they saw the Lord. 21 Jesus said to them again, “Peace be with you. As jthe Father has sent me, even so I am sending you.” 22 And when he had said this, he breathed on them and said to them, “Receive the Holy Spirit. 23 If you forgive the sins of any, they are forgiven them; if you withhold forgiveness from any, it is withheld.”
24 Now Thomas, one of the Twelve, called the Twin, was not with them when Jesus came. 25 So the other disciples told him, “We have seen the Lord.” But he said to them, “Unless I see in his hands the mark of the nails, and place my finger into the mark of the nails, and place my hand into his side, I will never believe.”
26 Eight days later, his disciples were inside again, and Thomas was with them. Although the doors were locked, Jesus came and stood among them and said, “Peace be with you.” 27 Then he said to Thomas, “Put your finger here, and see my hands; and put out your hand, and place it in my side. Do not disbelieve, but believe.” 28 Thomas answered him, “My Lord and my God!” 29 Jesus said to him, “Have you believed because you have seen me? Blessed are those who have not seen and yet have believed.”
30 Now Jesus did many other signs in the presence of the disciples, which are not written in this book; 31 wbut these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.
Notice, they could forgive sin. They no longer had to go to the temple and make offerings. This was the change from the OT to the NT. Where they are given the power to forgive sin. This was their empowering….. it happened prior to the Ascension and before Pentecost. Yet they tarried till Pentecost with the other believers...