Could you please show this in the Bible?
Acts 16:29 Then he called for a light, and sprang in, and came trembling, and fell down before Paul and Silas,
30 And brought them out, and said, Sirs, what must I do to be saved?
31 And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
32 And they spake unto him the word of the Lord, and to all that were in his house.
33 And he took them the same hour of the night, and washed their stripes; and was baptized, he and all his, straightway.
34 And when he had brought them into his house, he set meat before them, and rejoiced, believing in God with all his house.
What did the Philipian jailer ask Paul and Silas? He asked "What must I do to be SAVED". Now what does that mean, SAVED?
Obviously this man realized he was a sinner and was in danger of eternal damnation. He wanted to be forgiven his sins, he wanted to be reconciled with God, he wanted to escape punishment.
The Philipian jailer was sincere, he wanted to be saved, and he wanted to be reconciled with God. He did not turn away, he believed as well as all his house.
You insist this fellow only wanted to know how to escape judgment. I would like to know how you know that? Do you believe that because some Reformed theologian said that because this passage absolutely refutes Calvinism? Probably. But the fact is, he wanted more than just to escape punishment, he wanted to be reconciled with God, and the proof is that he believed.
Cornelius is another example. He was devout, he feared God. He gave much alms and prayed always. Yet he was not saved, because the angel that appeared to him told him to send for Peter where he would hear words whereby he and his household would be saved.
You would probably argue again that Cornelius simply wanted to escape judgment. Well, if so, then he fooled God himself, because God sent an angel to him to tell him how to be saved.
You will go to any extreme to hold to Calvinism, even rejecting scriptures that clearly refute your pulled from context proof texts. Cornelius sought God, and he was sincere. So sincere that God sent an angel to him. But he was not regenerated until he heard the gospel from Peter and believed on Jesus.
Believe whatever you want, but it is not scriptural to say the unregenerate cannot seek God, both Cornelius and the Philipian jailer refute this false doctrine. They were not only able, they in reality sought God and found him.