An Air Carrier on initial climb reported a NMAC with a Helicopter ATC had previously warned them of.

Narrative

We were assigned and departed from Runway X [at] ZZZ. Just prior to our Takeoff Clearance the Tower Controller was talking to a helicopter making him aware of our impending departure and cautioned him for Wake Turbulence. The helicopter confirmed and then the Tower Controller cleared us for Takeoff and made an advisory note to us about the helicopter was 2nm NW of the field traveling east on the shore line and that he would be at 300 ft. He DID NOT tell us to maintain visual separation from the helicopter and we did not say anything other than a confirmation that we understood the traffic information. I didn't think anything was out of the ordinary with the information being it was a helicopter 2 miles away.The aircraft was heavy (near max gross takeoff weight (structural)). This resulted in a lot of Runway used for departure. We used about 7000 ft. of Runway by the time we had weight off wheels. We were assigned the ZZZZZ [departure] which is Heading 078° to 520 ft. left turn 320° just as I began the turn to 320° I saw the helicopter out window. I was unable to see the helicopter prior to the turn or on the departure due to the trees.The helicopter went directly below our aircraft and I looked back at the TCAS and saw that we had 300 ft. separation at that time. We continued our left turn to the 350° heading. We never received a traffic alert from the Controller. And continued the departure normally.