The Bible teaches election.
1Pe 1:2 elect according to the foreknowledge of God the Father, in sanctification of the Spirit, for obedience and sprinkling of the blood of Jesus Christ: Grace to you and peace be multiplied.
The Bible teaches man is responsible.
Act 17:30 "Truly, these times of ignorance God overlooked, but now commands all men everywhere to repent,
The Bible teaches man can resist the Holy Spirit.
Mat 23:37 "O Jerusalem, Jerusalem, the one who kills the prophets and stones those who are sent to her! How often I wanted to gather your children together, as a hen gathers her chicks under [her] wings, but you were not willing!
The Bible teaches that God reveals Himself to all people.
Rom 1:21 because, although they knew God, they did not glorify [Him] as God, nor were thankful, but became futile in their thoughts, and their foolish hearts were darkened.
Election, free will, responsibility are all a part of God's plan and we have to accept each one even though they do not seem to be compatible.
Someday we will not see dimly as we do now, but God will reveal all things to us and we will understand. But for now, we have to accept all things through faith whether we understand them or not.