Air Carrier flight crew reported TCAS RA on initial climbout from SAV airport.

Narrative

While holding in position on runway; ATC issued modified takeoff clearance to turn right heading 010 and climb to 2;000 feet after takeoff as opposed to runway heading 3;000. After taking off in VMC conditions; as briefed; the Captain (PF (Pilot Flying)) initiated a right turn to 010. Climbing through 1600 we received a 'traffic traffic' warning from TCAS. Concurrently ATC advised us of the traffic but did not issue an alert. We had visual contact with the traffic at that point. Through 1700; the resolution advisory started; saying 'level off level off'. The Captain leveled off at 2000 and rolled out on heading 010. I advised ATC that we were complying with a TCAS resolution advisory and were level. The traffic passed approximately 500 ft. above from left to right; and TCAS announced clear of conflict. I advised ATC we were clear of conflict and they issued a climb to 10;000 ft. on the same heading; ending the event.As far as we could tell; ATC could have cleared us for takeoff straight out and then turned us behind the traffic.Given our departure off of Runway 28 and our initial fix of JROSS; which was nearly the opposite direction; ATC may have been trying to give us a shortcut by modifying our climb clearance to 2;000 instead of 3;000 so they could immediately turn us closer to JROSS. It is unclear whether the Controller planned for us to turn inside or outside of the traffic; however we ending up going nearly right under the traffic; and seemingly with less than required vertical separation. This conflict was unavoidable given the clearance received.