I'm sorry but I don't see a contradiction between what Peter says in Acts 2:38 and the events recorded in Acts 10. Maybe if you were specific about what contradiction you see there I could explain why I don't see it as a contradiction.
Acts 2:38
38 Peter
said to them, Repent, and each of you be baptized in the name of Jesus Christ for the forgiveness of your sins; and you will receive the gift of the Holy Spirit.
1. Repent. First step mentioned by Peter. Repentance is only possible through faith, consequently, faith is first.
2. each of you be baptized in the name of Jesus Christ for the forgiveness of your sins- According to your interpretation, Peter is saying that baptism is for the forgiveness of sins.
3. and you will receive the gift of the Holy Spirit.- According to your interpretation, the Holy Spirit is given as result of baptism.
Acts 10
43 Of Him all the prophets bear witness that through His name everyone who believes in Him receives forgiveness of sins.
Here Peter tells us that the forgiveness of sins comes from faith. Baptism is not mentioned which would be a contradiction IF baptism is the vessel for the forgiveness of sins.
44 While Peter was still speaking these words, the Holy Spirit fell upon all those who were listening to the message.
The Holy Spirit is given prior to baptism which would be a contradiction if the Holy Spirit is given as part of baptism.
45 All the circumcised believers who came with Peter were amazed, because the gift of the Holy Spirit had been poured out on the Gentiles also.
Both believing Jews and gentiles received the Holy Spirit through faith not through baptism. The heart is regenerated prior to baptism to effect faith.
46 For they were hearing them speaking with tongues and exalting God. Then Peter answered,
Peter spoke in tongues just he did during Pentecost.
47 Surely no one can refuse the water for these to be baptized who have received the Holy Spirit just as we did, can he?
Peter equates the desire of being baptized with receiving the Holy Spirit and Peter tells them that what they are experiencing is identical to theirs. In other words, the order is regeneration, faith, repentance, the receiving of the Holy Spirit, and then baptism.
48 And he ordered them to be baptized in the name of Jesus Christ. Then they asked him to stay on for a few days.
The believers which already had faith already, who had already repented, who had already received the Holy Spirit, who were already regenerated, then received baptism.
If regeneration and forgiveness of sin are effected by baptism then Peter did indeed contradict himself.
Here are a few other verses where sins have been forgiven through faith and apart from baptism.
Matthew 9:2
2 And they brought to Him a paralytic lying on a bed. Seeing their faith, Jesus said to the paralytic, Take courage, [
a]son; your sins are forgiven.
Matt. 26:28
28 for this is My blood of the covenant, which is poured out for many for forgiveness of sins.
Luke 5:20
20 Seeing their faith, He said, [
a]Friend, your sins are forgiven you.
Acts 13:38
Therefore let it be known to you, brethren, that through [
p]Him forgiveness of sins is proclaimed to you, 39 and [
q]through Him everyone who believes is [
r]freed [
s]from all things, from which you could not be [
t]freed [
u]through the Law of Moses.
Col. 1:13-14
13 [
t]For He rescued us from the [
u]domain of darkness, and transferred us to the kingdom of [
v]His beloved Son, 14 in whom we have redemption, the forgiveness of sins.
1 John 2:12
12 I am writing to you, little children, because your sins have been forgiven you for His names sake.
In addition to the above verses, the whole concept of salvation is fully dependent upon faith. There is no baptismal condition for salvation any where in scripture. I know that you deny that baptism saves but your words attest differently. I think that your theology is Lutheran since they have the same wavering of belief regarding baptism. It's necessary but is not. Salvation is by faith alone. Nothing else is co-required. Remission of sins is through Jesus blood. Nothing else is co-required.