You need to focus on building thickness. Building overall mass in your back. This in turn will make your lats wider and bigger in time.
The best way is to learn proper back training technique which most ppl dont use. (Thats why 99% of lifters dont have any back)
Seated low rows
Seated rows: Focus on retracting your shoulder blades as you move the weight. You cant simply move the stack from A to B as this will involve mostly arms. Keep your elbows low to your side.
When you perform pull downs, angle your elbows slightly forward. This will engage your lats immediately. Try it on yourself while ur sitting at the desk. The minute you move and flare your elbows to the side, ur no longer using your back, but rather ur shoulders.
This is prob the best i can do without giving you a one on one session where id promise to tear your back up so much youd think you had a piano on your back 24/7 😉