How can a fallen and unregenerate man do anything that would glorify God?
10: As it is written, There is none righteous, no, not one:
11: There is none that understandeth, there is none that seeketh after God.
12: They are all gone out of the way, they are together become unprofitable; there is none that doeth good, no, not one.
He can't on his own. Yet, God has made Himself known to man (Rom.1:19), He has made it possible for man to seek him (Acts 17:27), God desires all men to be saved (1Tim.2:4,2Pet.3:9), has paid the price of sin for all men (1Jn.2:2, 1Tim.4:10) and will shine His light in them to show them the truth (2Cor.4:6).
Their response to that truth is their responsibilty, and choice (that God always knew). It is an act of faith (acceptance) of the free gift offered to them in the Person and Work of the Lord Jesus Christ. If one believes and accepts the offer, no merit is given to him, but the one who is doing the offering, who bought and paid for the gift (Rom.4:4-5,1Pet.1:18:19)