Air carrier First Officer reported a GPWS terrain warning while on a night visual approach inside the FAF. Flight crew continued the approach without following the terrain avoidance procedure and landed.

Narrative

While cleared for the visual; backed up and established on the RNAVXX; in night VMC; we received a TOO LOW TERRAIN" caution past the final approach fix. The captain as PF said it was fine and elected to continue the approach without performing the terrain avoidance procedure. We then landed without incident. Given a clearance to descend below 10;000 ft; the captain as PF was flying at 300 kts in an FMS vertical mode with an altitude restriction of 11;000ft at a fix several miles out in the FMS. I mentioned to the captain if he knew that the airplane was going to level at 11;000 and remain at 300 kts passing through 12;000. He was not aware of this; then selected FPA and manual speed 250. I then explained he will have to arrest the descent angle sometime before 10;000 because even with full speed brakes it's not going to slow in time. He then selected green FLCH but it was too late for the given decent rate. He managed to level the airplane around 9;700ft and slowed to 250 kts before continuing the descent. After the fact reviewing our SOP; we should have performed the terrain avoidance procedure. Although in VMC; on a stabilized approach laterally/vertically; and adequate visual references ensuring impact into terrain was not going to occur; this approach was flown at night and our SOP states the avoidance procedure is required when given a "TOO LOW TERRAIN" in IMC or night. Air carrier First Officer reported a GPWS terrain warning while on a night visual approach inside the FAF. Flight crew continued the approach without following the terrain avoidance procedure and landed."