An air carrier pilot reported on initial climb from BLI they took evasive action to avoid a conflict with two VFR aircraft operating in the pattern. BLI Tower closes during scheduled operating hours due to controller staffing.

Narrative

While on departure during closed Tower operations we received a clearance from Victoria Terminal. Through our CTAF calls we knew there was one VFR aircraft on the downwind but had not heard from any other aircraft. We had a quick discussion prior to starting our takeoff roll on what we saw on TCAS and did not see anyone on our departure route. On departure we picked up two more TCAS targets between 1000 ft. and 3000 ft. I (right seat) visually acquired an aircraft approximately one mile to the right; level with us; and turning towards us. Simultaneously the Captain picked up a second aircraft 500 above us and descending directly on our path. This resulted in a TCAS TA. The choice was made to maneuver left off the SID and level to gain separation as we were still not talking to a Controller. Both pilots were padlocked on targets and lost SA inside the aircraft; resulting in a momentary Flap Overspeed. After clearing both targets to the south we rejoined the SID and made contact with Victoria. VERIFIED WRITE UP. BLI is much too busy an airport to have an unmanned Tower. There were two jets; two turboprops; and at least three piston aircraft in the area. Some of the confusion came from the calm winds resulting in no obvious runway choice.