Well they shouldn't make noise, old or not. I've bought new bikes and had bikes repaired that have had stuff misadjusted right out of the box, so to speak, that's always possible. Recently bought a new bike for my wife with disk brakes the front was rubbing right off the bat. & supposedly assembled by knowledgeable mechanic? Twice I've had bottom brackets replaced and the press fit cranks were not tightened.

Properly adjusted bike should not have any clicking, ticking, creaking or squeaking. There might be normal chain noise you hear when riding next to a wall, etc. that comes from the chain wrapping through the RD.

For reasons I listed, I now do most of my own mechanics. There are numerous videos out there on adjusting your derailleurs, etc, (I highly recommend the Park Tool videos).

I would ride the bike a few more times, making sure you shift into a few different gears front and back (IOW work the cables). Then take it to the shop and let them adjust it. Cables will stretch after a while on a new bike but yours sounds like it wasn't right from the start.

If its making a constant ticking its most likely the rear derailleur need adjusting, especially if it sounds like it coming from back there. If the clicking is directly below you, it might be the cranks need tightening.