In regards to scripture, as far as I can tell, every baptism is preceded by instruction in the faith, none are immediate. Lent is the period that was for baptismal instruction... I don't see how tradition is being made up.
However, the reason that Baptisms were only once a year in the early church was that there were simply not enough Bishops to go around. Only Bishops baptized in the beginning, so people had to wait until the Easter Vigil.
All matters with waiting and Lent aside, I have question to throw out about baptism. I have read a few times that we don't know if unbaptized babies are saved.... but how do we know that baptized babies are saved? Does Baptism save us?
There
are instances of people being baptized immediately. Ever after just a brief encounter. So saying none were immediate is a misnomer. None of the baptisms were preceded by extensive training in Christianity. Even though it might be adiaphora there is nothing saying that baptism can't be immediate. We can't speculate on what God's mercy is for unbaptised children so therefore it wouldn't be wise to take a chance and wait. We can't speculate on what is NOT written.
Acts 8:37-39 (New King James Version)
37 Then Philip said, If you believe with all your heart, you may.
And he answered and said, I believe that Jesus Christ is the Son of God.[
a]
38 So he commanded the chariot to stand still. And both Philip and the eunuch went down into the water, and he baptized him. 39 Now when they came up out of the water, the Spirit of the Lord caught Philip away, so that the eunuch saw him no more; and he went on his way rejoicing.
Acts 9:17-19 (New King James Version)
17 And Ananias went his way and entered the house; and laying his hands on him he said, Brother Saul, the Lord Jesus,[
a] who appeared to you on the road as you came, has sent me that you may receive your sight and be filled with the Holy Spirit. 18 Immediately there fell from his eyes
something like scales, and he received his sight at once; and he arose and was baptized.
19 So when he had received food, he was strengthened. Then Saul spent some days with the disciples at Damascus.
Acts 16:32-34 (New King James Version)
32 Then they spoke the word of the Lord to him and to all who were in his house. 33 And he took them
the same hour of the night and washed
their stripes. And immediately he and all his
family were baptized. 34 Now when he had brought them into his house, he set food before them; and he rejoiced, having believed in God with all his household.
Acts 19:4-6 (New King James Version)
4 Then Paul said, John indeed baptized with a baptism of repentance, saying to the people that they should believe on Him who would come after him, that is, on Christ Jesus.
5 When they heard
this, they were baptized in the name of the Lord Jesus. 6 And when Paul had laid hands on them, the Holy Spirit came upon them, and they spoke with tongues and prophesied.