Faith is obedience. Men have been commanded to believe. So when men do choose to obey that command by believing then that belief/faith is obedience.
Belief in the NT is not just a mental assent of the mind, it is not just an acknowledgement of certain facts but belief is a word of action. A person can believe, acknowledge that Christ died for him but unless, until he obeys Christ Heb 5:9 and does the things Christ says Luke 6:46 then that belief is dead and worthless.
Faith is not obedience. Faith, according to the dictionary, is complete trust or confidence in something or someone. Obedience (belief) is submission to authority. One has to put their trust in Christ (faith) and submit to His authority (obedience).
Men have been commanded to believe. The simple fact is, unless God changes the heart they will not. We are by nature steeped in rebellion to God and our hearts are evil and deceitful. Faith (or trust in Christ) is a gift from God where He opens our eyes and ears to hear the gospel and respond to His calling. And it is important to note that there are degrees of faith (or trust in the Lord) given to us by the Spirit.
Ephesians 2:8 For by grace you have been saved through faith. And this is not your own doing; it is the gift of God
1 Corinthians 12:9 to another faith by the same Spirit, to another gifts of healing by the one Spirit
Obedience is our adhering to that gift. Because of our rebellious heart, God has put His Spirit within us, to walk according to His ordiances and statutes.
Ezekiel 36:26 And I will give you a new heart, and a new spirit I will put within you. And I will remove the heart of stone from your flesh and give you a heart of flesh.
So both faith and obedience are gifts given to us by God.