Wait, I said this was about cold water, but let’s get sneaky. Sometimes your hot water heater has a rusted-out anode rod, and that sediment sneaks into the cold line through a cross-connection. Yes, that’s a real thing.
Or, your water heater might be dying. If the brown water smells like rotten eggs, that’s sulfur bacteria—not your emergency. But still, run the water for a while and see if the smell disappears.
Bottom line: if the brown only shows up when you use hot water, your heater is the drama queen. If it’s only cold water, it’s almost always from the city or your main pipe.