This noise is "normal" and is extremely unlikely to ever go away. You can get good info from USMB.net on all kinds of Subarus. If the noise goes away, is it perhaps the "piston slap" that so many of the EJ25 engines have? In either case, if the sound goes away once warm you've nothing to worry about. Thousands (millions?) of Subarus sound that way and will still run perfectly for another 250,000 miles (or more).
I'm sorry; I did not answer your question. Subaru quit using hydraulic lash adjusters in the EJ25D for the '97 model year. That means yours are not hydraulic and I suppose <i>could</i> be part of the problem. Subaru also shortened the piston skirts for that year and that's when the "piston slap" noises started. That's what I suspect you have, and like I said as long as it goes away once the engine is warm, everything will be fine.