EMB-145 First Officer reported executing a missed approach after receiving a GPWS Sink Rate during a non-precision continuous descent final approach.

Narrative

Sink Rate GPWS Callout triggers Missed Approach ASOS weather at ZZZ1 advertised visibility greater than minimums required for the RNAV XX (LNAV only). The Precision Approach Path Indicator for runway XX were NOTAM out of service. The flight crew conducted an approach using a CDFA to the published minimums rounded up to the next 100 ft increment (700 ft MSL). The aircraft was flown on or around the FPA (Flight Path Angle) to ZZZ; and the aircraft sequenced to ASEL to capture 700 ft MSL. Upon leveling at 700ft; the flight crew established visual contact with the runway environment; disconnected the autopilot; and continued the visual segment of the approach. Due to the lack of functional PAPI lights and the momentary arresting of the CDFA; the aircraft was effectively high of the desired glide path and a higher than normal rate of descent was required to return the aircraft to the glide path. This momentary increase in the descent triggered a GPWS 'Sink Rate' aural alert; and the crew immediately initiated the Go-Around/Missed-Approach procedure. After the initiation of the TO/GA sub-mode while the aircraft was rotating to a go-around pitch attitude; the GPWS gave a 'Don\'t Sink' call. The aircraft climbed without incident to the missed approach altitude following the missed approach track; and was subsequently vectored back for an additional approach.suggestion: Without LNAV/VNAV capability; implement procedures such as a derived decision altitude to allow for CDFA when weather is at/near LNAV minimums without a level-off at rounded-up minimums.