There certainly are plenty of trout on the Olympic Peninsula waters. We don't have the kind of "resident" trout fishing that many other regions enjoy, but we do have enough to keep most fishermen happy, if they are willing to do the work. There are cutthroat that never stay from the streams or lakes, and there are cutthroat that go to sea every spring, to return in the later summer or fall. And there are some resident rainbows, (termed "residualized steelhead"), that are caught on occasion. And we do have some summer steelhead. There's Bull Trout too. And some of the mountain lakes have some brook trout left. The beaches have good fishing for sea-run coastal cutthroat trout too.
Here are a few suggestions to get you started:
https://www.amazon.com/Fly-Fishing-Guide-Olympic-Peninsula-Doug/dp/157188419X
https://www.amazon.com/Fishing-Olym...8986371&sr=1-2&keywords=Doug+Rose+fly+fishing
https://www.amazon.com/Steelhead-Fl...8986467&sr=1-3&keywords=Doug+Rose+fly+fishing
Doug is gone now. But he left behind a good body of work on the Olympic Peninsula fly fishing life. You will do well to read his works. He will lead you to the trout.
If you do some searching on these forum pages you will find trip reports, stories, and plenty of information about fishing out here at the end of the road. Most of us have had to work long and hard to find the fishing that we did. So don't be surprised if people are not too quick to hand it over to you easily online.
http://olympicpeninsulaflyfishing.blogspot.com