"Surfing the internet" became a thing in the early 1990s (here's the earliest use of "surf" in that sense, in a 1992 usenet post), according to the OED. "Channel surfing" (on a TV) started to be used in the mid-1980s according to this informal investigation.

I suspect the discussion of train-surfing, van-surfing etc in my second link is a red herring. More probably the phrase "surfing channels" is based on analogy with "skip" or "hop" - as in skipping channels, skipping the rails, skipping a gate, skipping stones. That seems intuitively likely since all three terms - "surf", "skip", "hop" - can convey the sense of passing over something while barely touching it or interacting with it only superficially. It'd be hard to prove that definitively though.