Fractional First Officer reported an unstable approach leading to a sink rate call by the aircraft.

Narrative

We were cleared for a visual approach to Runway XX at ZZZ. ATC requested that we keep our base within 6 nm of the approach end of Runway XX due to traffic spacing. In order to 'help out ATC we accepted the clearance. We were initially high and fast; so the pilot flying (PF) elected to slow by dropping the gear early; and extend the spoilers. This allowed us to lose altitude and try and slow as we made a 5 nm left base. We also configured on speed with Flaps 20; and then Flaps 30. After we extended the flaps to 30 (with the gear and spoilers extended) it began to look like we would be stable by 500 ft. This made it feel similar to the approach that we had into ZZZ1 on the previous leg. As we approached 600 feet the PF stowed the spoilers; expecting the drag from flaps and gear extended; and with idle throttles to allow us to be stable by 500 ft. Nearing 500 ft; the PF noticed the auto throttles may have gone above IDLE power; keeping us slightly faster than anticipated. When the PF pulled back on the thrust levers to ensure they were at idle the auto throttles automatically disengaged. With idle to near idle power to correct the speed; and descending to the runway; we received a sink rate aural warning due to a momentary increase in descent rate. The PF adjusted pitch to reduce our descent rate; eventually getting to vref by the threshold. We landed within the touchdown zone of the runway and exited well before the end.The approach was steeper than expected for a visual into the flat terrain of ZZZ. The Auto throttle disengagement annunciation.Pilot monitoring (PM) crosscheck of instrumentsCause: Attempt to satisfy or exceed ATC request for a short approach; despite being high on energy (high and fast)Lack of recent flying in the aircraft by the PF. 2 or 3 legs in the last 2-3 months.Lack of recent auto throttle experience by PF. 2-3 legs in 6 months or more.Successful previous steep approach into ZZZ1 on the previous leg.We put ourselves in a position to make an unnecessary steep approach; which delayed getting stable to about 500 ft. Despite being able to make it work; an issue with the auto throttle put our speed near (and possibly slightly over) the vref +10 at 500 ft. If so; we should've gone around. Suggestions: Don't accept a steep approach from when it's not needed. Especially to just help ATC. Request additional vectors; or simply go missed early. Don't let your guard down on the auto throttles. They can easily put you in a bad situation if you don't constantly monitor them and ensure they are doing what you want as the PF. If you think you might've been outside a stabilized approach parameter; just go around and try it again."