Air carrier flight crew reported a sudden Wind Shear Encounter during final approach in which the Captain took immediate evasive action. After completing the appropriate procedures a safe landing was completed.

Narrative

On approach to ZZZ (about 500 ft. AGL) in VFR conditions; suddenly; airspeed became erratic and the aircraft began to roll right and yaw left. The Captain called for a go-around; so I immediately complied. When the aircraft failed to gain altitude; the Captain called for the controls and fire walled the thrust levers. He was able to maintain aircraft attitude incredibly well considering the circumstances and gained a positive rate without changing configuration (exactly what the company profile for wind shear escape calls for). At a safe airspeed and altitude we retracted flaps and gear normally and completed the necessary checklists to begin a second attempt. The airport updated the ATIS two minutes after our go around. The previous ATIS did not warn or advise of LLWS or PIREPs. Although a C130 did execute an unannounced go around at ZZZ while we were on approach. Perhaps unrelated; but the C130's reason for going around was never made clear. We also experienced an FMS computer malfunction while setting up for the second approach but were able to safely land regardless. The wind shear alert in the aircraft never activated although the situation did present textbook sudden wind shear symptoms.