rotten egg smell in cold water only bathroom sink of new home
We had this same problem. The smell was only coming from our kitchen sink, and only for a few seconds after the water was turned on.  No other faucet in the house had smelly water, so I was quite certain it wasn’t from water heater issues. We tried draining some water from the water heater just in case, but no sediment came out and no smell. Since the smell only lasted a few seconds at the faucet, I figured the smell had to be building up somewhere between the water heater and the offending sink.

What I eventually noticed was that the braided pipes leading to the hot and cold had subtle horizontal “S” curves in them where smelly gas could get trapped, like how a toilet is shaped so sewer gas doesn’t come back up. I figured that when the water hadn’t been run in awhile, the gas would build up in the upper curve. Then the water would push the gas out when it was turned on. So I replaced the braided pipes with shorter ones that didn’t crate that “S” curve. We have been smell free ever since.