G650 First Officer reported on climb out taking evasive action to avoid a helicopter resulted in a NMAC.

Narrative

Departing Runway XX at ZZZ we were given a right turn to a 350 heading on departure; maintain 2000. There was no traffic reported specifically to us; but there was background radio traffic in contact with the Tower that I could hear; but I was not aware of their position. On line up I noted several ads-b traffic targets on the Multi-function Flight Display (MFD) that were in the vicinity of the ZZZ VOR that I didn't deem a threat because of our assigned turn. After rotation; as I was executing PM duties (disarming ground spoilers; and selecting the new heading on the guidance panel) the PF initiated the expected right hand turn. As he did so; he simultaneously called out 'Helicopter' while increasing the rate of turn and decreasing the rate of climb from approximately 4000fpm to zero as the TCAS was commanding a 'Level Off' RA. After successfully avoiding the helicopter; the climb continued as scheduled. During the event; the helicopter called out that he was maneuvering to avoid a collision. I noted his trend on the TCAS display as continuing to descend the entire time; and visually out the window he appeared to be attempting to turn away from us while maintaining a high descent rate. Tower should have made us aware of a helicopter descending to the airport; especially one that was going to be to the north of the departure end of the runway; given our heading assignment. The reality is that the Tower has zero control of the helicopters and seaplanes that operate out of ZZZ1. It's essentially a free for all; where everyone goes where they want; and they do what they want. The Tower really only issues clearances; without doing an adequate job of maintaining separation.