C-185 floatplane Captain reported a NMAC event during initial climb with an non-reporting landing aircraft. The floatplane Captain took immediate evasive action to avoid a collision.

Narrative

Flight was an organization orientation flight departing ZZZ; in a Cessna 185 floatplane. The passenger had switched seats from and earlier flight; before casting off from the NW Public Dock at ZZZ. The primary flow of floatplane traffic for the afternoon had been taking off and landing to the SW on XXW. Local ATIS was obtained; and reported to ZZZ Radio at Startup; along with our planned departure; waterway; and direction of flight to the northwest along the shoreline for our northbound VFR routing. The departure ATIS was reporting winds light with no preferential runway; a change from the prior hours suggested SW landing on XXW. Our takeoff was announced on CTAF; and ZZZ Radio didn't report any inbound traffic for our departure or routing. No inbound radio calls were heard on the CTAF.Takeoff was performed to the SW off waterway XXW. After departure and setting cruise climb power; and passing 1;100 ft MSL/AGL; flight controls were being transferred to the passenger as part of their orientation flight. I looked down to observe the passenger taking the Yoke; looked up and saw a near coaltitude float equipped turbine Otter at approximately 500 ft at our 1230 relative position. I immediately resumed full control of the airplane and banked left; extend for around 10 seconds; then rolled back to observe the Otter. From my perspective after turning back; the Otter hadn't altered its flightpath. Within the minute of the event; an aircraft reported on final for the water; and our depart and route was reported by ZZZ Radio to the reporting aircraft.The organization aircraft being flown has ADSB IN and OUT installed. The airplane is equipped with a Garmin 650 GPS and an additional Garmin 275 Traffic display. Bother units were operational and in use. No ADSB 'Traffic Alert' was aurally announced or displayed throughout the event. All exterior light were in use; i.e.: LED Taxi/Land Lights in Pulse mode; LED Nav Position lights were ON and Strobe Lights were all ON.Recommended Self-announced radio calls from the Otter approaching the seaplane base would have helped prevent this event. Use of ADSB out by the Otter would also have helped.A potential midair was avoided only through 'see and avoid.'