Peter was not the first to speak, the debate was well in progress when he spoke up. Peter made no final decision. Paul and Barnabas spoke afterward.
Why would there need to be more discussion on the signs and wonders within the gentile community if the issue was settled at that point?
1
Some who had come down from Judea were instructing the brothers, “Unless you are circumcised according to the Mosaic practice, you cannot be saved.”
You see Portrait, Ginger2 was right! Peter was not the first to speak - there was this group that were actually discussing the topic before Peter spoke. While this may have been a literary style to introduce the reader to what was coming next, I will have to agree with Ginger2 on the speaking order!

Even though this discussion took place outside of the actual Council, the assumption would be that these guys were still talking about the topic! But, now, the plot thickens…
2
Because there arose no little dissension and debate by Paul and Barnabas with them, it was decided that Paul, Barnabas, and some of the others should go up to Jerusalem to the apostles and presbyters about this question.
3
They were sent on their journey by the church, and passed through Phoenicia and Samaria telling of the conversion of the Gentiles, and brought great joy to all the brothers.
4
When they arrived in Jerusalem, they were welcomed by the church, as well as by the apostles and the presbyters, and they reported what God had done with them.
5
But some from the party of the Pharisees who had become believers stood up and said, “It is necessary to circumcise them and direct them to observe the Mosaic law.”
And here we have a specific group who gets up in the Council and speaks before Peter. Ginger2, it looks like you were right again. Now, I know they did not have ‘Roberts Rules of Order’ back in 51AD - but, it certainly sounds like the Pharisee is making a motion to be discussed (no doubt he got a ‘second’ to his motion) Let’s see what happens…
6
The apostles and the presbyters met together to see about this matter.
7
After much debate had taken place, Peter got up and said to them, "My brothers, you are well aware that from early days God made his choice among you that through my mouth the Gentiles would hear the word of the gospel and believe.
So, in modern terms … a motion was made and seconded and there was a debate - and here is where we make this radical shift from a parlamentary type meeting to one where God is leading the Council through His Chosen Leader" Peter. It is Peter who NOW speaks, ending further debate by making the decision. And, this is the point you may want to foucus ont, Ginger2: Peter gives an explanation citing God as the source.
8
And God, who knows the heart, bore witness by granting them the holy Spirit just as he did us.
9
He made no distinction between us and them, for by faith he purified their hearts.
10
Why, then, are you now putting God to the test by placing on the shoulders of the disciples a yoke that neither our ancestors nor we have been able to bear?
11
On the contrary, we believe that we are saved through the grace of the Lord Jesus, in the same way as they."
So, let’s make sure we got this straight: God has shown Peter that Gentiles are to be admitted without having to be circumcised. Peter publically chides them for not being open to God’s Spirit as is being made known. Peter does not pull any punches - and tells them that we could not follow the Law of Moses, either! (You see, it just was not circumcision…

there were all of these Sabbath laws that someone had to keep!
12
The whole assembly fell silent, and they listened while Paul and Barnabas described the signs and wonders God had worked among the Gentiles through them.
Just in case anyone missed this - the Holy Spirit did not just work through Peter (Acts 10) in freeing the Gentiles from the Law of Moses - here are two more witnesses. This matter had been resolved by Peter and here we have Paul and Barnabas putting some icing on the cake…
13
After they had fallen silent, James responded, "My brothers, listen to me.
14
Symeon has described how God first concerned himself with acquiring from among the Gentiles a people for his name.
Another way to look at this is James is saying, “Hey! I agree, too!” But, the deed is done and James is just bringing up the rear.
God bless