If someone has genuine saving faith in Christ and have received the Holy Spirit, it would be impossible for them to have NO love at all. Paul uses hyperbole (obvious and intentional exaggeration) about understanding ALL mysteries and ALL knowledge and having faith that can move mountains yet having NO love.
Paul is not exaggerating about the importance of love though. Faith works through love (Galatians 5:6), but we are saved through faith, not faith plus love. Love is the greater quality of the three because God is love and it outlasts them all. Long after faith and hope are no longer necessary, love will still be the governing principle that controls all that God and his redeemed people are and do. We won't need faith and hope in heaven.
So Paul is not teaching that even if our faith is genuine that our faith cannot save us without producing "enough" love. Paul is stressing the importance of love, not teaching that faith is insufficient to save us without our best efforts to love. All genuine BELIEVERS love Christ. Why? Because we have received the love of God in our hearts by the Holy Spirit who was given to us (Romans 5:5) when we believed the gospel (Ephesians 1:13). We love Him because He first loved us (1 John 4:19).
It is not only hyperbole, Paul has made it clear that love and faith are two different things. Love is not faith and faith is not love but love is the greatest of the two. You can have faith and not love. And it is not about loving God or Christ, it is the love for one another, for if we love one another, we love God.
But love for other people is a work and must be a work because we have to put effort. We can not love others only in our hearts, love is only full when the people that are loved fell loved and they will only feel loved through our actions and words (works).
It is, "Do to others what you would like them do to you", not, "feel for others what you would like them feel for you"
Faith in Christ is only foundational but Love is the identity in Christ. So faith alone doesn't save but being obedient to the command to love one another onto faith, then salvation is achieved.
Matt 25:
37“Then the righteous will answer him, ‘Lord, when did we see you hungry and feed you, or thirsty and give you something to drink?
38When did we see you a stranger and invite you in, or needing clothes and clothe you?
39When did we see you sick or in prison and go to visit you?’
40“The King will reply, ‘Truly I tell you, whatever you did for one of the least of these brothers and sisters of mine, you did for me.’