They did NOTHING to receive the Holy Spirit in salvation except believe what Peter was saying--no water baptism, no confessing Jesus as Lord. The speaking in tongues indicates that they have already been saved. They are not speaking in tongues in order to be saved. Their tongues indicate they are already saved:
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. 46 For they were hearing them speaking with tongues and exalting God." (Acts 10:45-46 NASB)
We do know for sure that Cornelius, like Abraham, obeyed the Voice of God, through God's messenger.
3 About the ninth hour of the day he saw clearly in a vision an angel of God coming in and saying to him, "Cornelius!"
4 And when he observed him, he was afraid, and said, "What is it, lord?" So he said to him, "Your prayers and your alms have come up for a memorial before God.
5 Now send men to Joppa, and send for Simon whose surname is Peter. 6 He is lodging with Simon, a tanner, whose house is by the sea. He will tell you what you must do." Acts 10:3-5
We know that Cornelius was instructed to send for Peter, who then would tell Cornelius what Cornelius must do.
Cornelius obeyed everything he was instructed to do, without obeying what God through His angel and through Peter, then Cornelius would not receive the salvation of that comes by faith.
We do know for sure that Cornelius was instructed to be Baptized, which is an outward expression of repentance.
Cornelius, like Abraham, obeyed the Voice of God.
Abraham, believed God when He told Abraham to get out of his own country to a land that He would show him.
Abraham obeyed.
Then while actually standing
in the place where God told him to go, God reaffirms His Promise to Abraham, to make him a great nation.
Then He brought him outside and said, "Look now toward heaven, and count the stars if you are able to number them." And He said to him, "So shall your descendants be."
And he believed in the Lord, and He accounted it to him for righteousness. Genesis 15:5-6
- Abraham, like Cornelius, had already demonstrated the obeying part of faith, when they believed.
Abraham was already in the promised land because he believed and demonstrated he believed by obeying the Voice of God
to go.
What Abraham was doing, in Genesis 15:6
was to continue to believe God, as he already obeyed by getting out of his father's house, and out of his own country, TO THE LAND THAT GOD WOULD SHOW HIM, AND MAKE HIM A GREAT NATION.
Make him a great nation = many, many descendants.
Likewise, Cornelius demonstrated the same obedience that faith requires, in obeying the Voice of God.
We don't know
what all Peter told him to do...
He will tell you what you must do.
We do know that Cornelius obeyed
what he must do.
We can clearly see that instantly Cornelius responded to what Peter preached, and was saved.
While Peter was still speaking these words, the Holy Spirit fell upon all those who heard the word. And those of the circumcision who believed were astonished, as many as came with Peter, because the gift of the Holy Spirit had been poured out on the Gentiles also.
For they heard them speak with tongues and magnify God. Then Peter answered, "Can anyone forbid water...
Acts 10:44-47
Those who came with Peter believed the Gentiles were saved,
BECAUSE they heard them speak with there mouth, in response to the preaching of Peter.
...with the mouth confession is made unto salvation.
Your mistake is to try and rule out that obedience is required in faith.
9 that
if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved.
10 For with the heart one believes unto righteousness, and
with the mouth confession is made unto salvation. Romans 10:9-10
Cornelius and his house had indeed turned to God, and were indeed using there mouth to magnify the Lord,
in response to Peter presenting the Gospel to them.
JLB
