I seem to recal that the Bible speaks to this.
Jesus Himself tells a story, (I believe it reads more like an EYEWITNESS account) Of a rich man and poor man. Both die. The poor man goes to Heaven, the rich to hades. The rich man is in torment, pleads for water and mercy, receives neither.
Further, he is told that no one will go back to warn his brothers. They have the same opportunity to believe or not.
For each man it is appointed to die, THEN (as in, after that)the Judgement.
So, while God is not bound by time, WE are bound by it. The time is NOW for all of us. WE have a decision, here and now, believe or dont. Having decidied, God honors that decision.
Hell isn’t Purgatory.
And prayers for mercy are prayers for mercy.
You seem to think that we are saying that prayer can change God’s mind and convert a dead, damned person into a saved person.
That’s not what we are saying at all. Purgatory is for the elect.