Air carrier First Officer reported taking evasive action to miss NORDO traffic on climb out; resulting in a NMAC.

Narrative

At approximately XA15 (late morning local); I had to execute an RA avoidance maneuver to comply with Company instruction and aircraft cues. We departed ZZZ on a normal climbout and in contact with Departure; when we were turned and given 'fly direct to ZZZZZ; climb and maintain 230 (may have been some other altitude; I did not take a note of it).' We were somewhere just north of ZZZZZ; climbing at 4000 fpm; at around 14;000 ft. when we received a momentary TA on our TCAS system. I was the Pilot Flying and called it out; but the Captain saw it at the same time. The TA was roughly; directly above us and slightly to the aircraft's left side of flight. The TA illuminated; but immediately went away.Around that time; ATC said they had a VFR aircraft in our vicinity that was not talking to ZZZ. While he was broadcasting; we received an RA; directly above us. I disengaged autopilot and autothrottle and started a descent per aircraft commands. The Captain directed I be more aggressive; as I was not meeting the 4000 fpm rate of descent that the aircraft commanded.Simultaneously; the Captain directed a right-hand turn. I immediately entered a right-hand turn; as well as descent; as I agreed with his assessment that the aircraft was above and to our left-hand side. I saw the RA get as close as 300 ft. before the RA disappeared and TCAS showed the aircraft behind us. The Captain then took the radios and informed ATC. There was momentary discussion as to why we were not warned and what happened. The ATC Controller seemed to be as surprised and shaken as we were. The rest of the flight to ZZZ1 was uneventful. I was fortunate to be flying with a good Captain; who handled the situation very well; in my opinion. His direction; experience; and instinct may have been what avoided catastrophe. Following discussion with ATC; the Captain informed the Passengers that we had to execute an aggressive descent per aircraft guidance; to ensure we stayed away from an aircraft that was not talking to ATC. He had to say something; as there was no way the Passengers didn't notice the abrupt change from climb to descent. Upon landing; the Passengers thanked us for the safe flight; and nobody commented or asked anything further about the descent. The Captain and I suspect an aircraft executing paradrop or jump operations. Our only explanation for a VFR aircraft descending into us at 14;000 ft. was a possible 'jump platform' chasing their jumpers back to the ground. Either way; I wanted to file this report to prevent another TCAS near miss; in the ZZZ area; in the future.