No one seeks God unless they have been given the grace of God's revelation. I expect, given your name, that what you are unwilling to say outright is your doctrine teaches no lost person is able to seek God until "enabled" by "Irresistible Grace."I think you are asking the wrong question here. It should not be, does God allow? It should be, who will seek? The answer is that nobody seeks God on their own. Romans 3:10-11.
So you have no answer to the fact 2 Thessalonians 2:13 says individuals are chosen for salvation "through" faith. That means they had faith which was utilized by God in His election of that individual. Thus they had to have sought God to have faith in God before they were even chosen. It is a lock.