Air taxi helicopter pilot reported an NMAC in Class G airspace requiring evasive action to avoid a possible collision.

Narrative

In cruise flight en route from to ZZZ; I spotted another aircraft head on at or near same altitude. I performed a right descending turn to avoid the other aircraft. I had been scanning inside and out for this traffic in TCAS; no target forward of our aircraft was visible on TCAS at the time and I had announced this to the crew and that I had other targets west across the river from us so I know it was working. TCAS did alert at the last split second as I was already in the turn. It appeared the other aircraft started a climb at the same time I spotted the aircraft and started my turn and descent. When we departed ZZZ1 we heard the other aircraft check on radio and report they were inbound to the hospital from the east. Radio comms advised them that we had lifted from ZZZ1 en route to base. They reported we were coming from the east had us on edge looking for them we knew our paths would cross at some point. With the position of the sun and haze and the fact that this aircraft was coming near head on made it very hard to see.