TRACON Controller reported vectoring an aircraft below the MVA towards a lower MVA and away from conflicting traffic. When clear of traffic ATC climbed the aircraft without further incident.

Narrative

Working all sectors combined. ZZZ Tower just opened and I released Aircraft X on ZZZZZ X SID. I was working out arrivals and departures to ZZZ1 and did not see conflict for Aircraft X until he was airborne climbing out of 025. Initial communication to Aircraft X was traffic alert and stopped his climb at 030 for unidentified aircraft indicating 040 converging (MVA is 040). I radared Aircraft X and turned him towards 030 MVA and gradually stepped up his altitude based on indicated alt from other aircraft. Aircraft Y called me and I identified him and immediately turned him away from Aircraft X. Aircraft Y was identified as an EC35; who reported Aircraft X in sight . I issued a low alt alert to Aircraft X and expedited his climb to 15000. The pilot of Aircraft Y said he had been in contact with the tower the whole time and wondered why they didn't 'ship him earlier so this whole thing could have been avoided'. The tower never communicated the traffic or the conflict to myself or Aircraft X prior to shipping the departure. Suggestion: The TRSA over the ZZZ airport does not provide adequate protection for departures off ZZZ. There is no communication or altitude requirement allowing non participating aircraft to fly directly into departure (and arrival corridors). The airspace needs to be updated to Class C to adapt to modern traffic requirements.Tower should have resolved a known conflict prior to launching Aircraft X. Tower should have issued traffic to Aircraft X. Tower should have transferred communication of Aircraft Y to me in time to resolve conflict and advised me that aircraft saw Aircraft X. Sectors could have been de combined sooner to allow for better scan.