I read a time travel story once that depicted them doing it over 3000 years ago
There really isn't any way to know how old anthropogenic burning is in the Northwest. We know from numerous sources that the natives burned often and that burning helped maintain the oak woodland/ oak savannah environments. For example, Tolmie reports at Fort Nisqually (near Tacoma) that the "the Indians are burning everywhere" in the early 1840's. At several occasions over several years he notes that the air is so smoky from native fires that you cant see 100 ft. Numerous vegetation studies have noted how natives kept fuel levels low and thus reduced the frequency of catastrophic wildire.
Burning at that scale can leave telltale horizons in certain soil profiles (charcoal flecking), so there is some physical evidence of precontact fire that is potentially datable. It is, however, impossible to discriminate between anthropogenic burning and natural wildfire in soil studies. It certainly wouldn't surprise me if human burning was that old, but, as I said, we really don't know.