The answer depends on what we mean by hear. The Bible teaches that God is all-knowing and all-present, so yes, technically he hears every word and thought of everyone.
But sometimes the Bible uses the word hear in regard to prayer to mean to answer it positively, with the yes we hoped for.
So will God grant the prayers of someone who is not a believer?
Surprisingly the Scripture doesn’t nail that down one way or the other. In fact, the Psalmist says of himself, “If I had cherished sin in my heart, the Lord would not have listened” (Psalm 66:18). This is why it is so important for a believer to moment by moment confess and turn from sin in their life.
On the other hand, in Acts 10:31 there is the story of the Roman centurion, Cornelius, who was told by an angel that “your prayer has been heard” though he was not yet a believer in Christ. He had not yet heard the gospel, though he obviously he had put faith in the true God to the extent he had learned from his Jewish friends.
This brings up an important point. Jesus said no one comes to Him unless he is first drawn by God (John 6:44), so God always makes the first move. But when does God start working on a person’s heart to open their eyes to the truth and draw them to Himself in Christ? And what if during that time they respond in prayer to Him in a number of ways: “God, if you real, help me know,” or “God, I’ve made a mess of my life, help me!” None of these are for salvation per se. But certainly God is helping! Many who are now believers can point back to prayers they prayed along the way to faith where God in fact did answer.
This drawing process was evidently going on in Cornelius’ life long before Peter arrived with the gospel. So, yes, clearly in some cases God does answer the prayers of someone who isn’t a believer in Christ.
Remember, God is sovereign. He has not painted himself into a corner on this one. Case in point, when Jesus was about to cast a whole “Legion” of demons out of the Gadarene man (Mark 5:1-13), they begged Jesus to send them into a herd of swine nearby rather than to a remote place. Jesus granted their request! Obviously demons aren’t even capable of being saved, yet Jesus, for His own reasons no doubt, granted that request.
What hinders our prayers from being answered? 1) We don’t actually ask (James 4:2), 2) We ask with wrong motives--for selfish pleasure (James 4:3), 3) We harbor unrepented unconfessed sin in our heart (Psalm 66:18), 4) We do not ask in faith (James 1:6-7), 5) We ask for things that are not God’s will (1 John 5:14-15), 6) We don’t ask in Jesus’ name --that is, trusting His authority and merit (John 14:13).