DIAGNOSIS That's usually trapped air in the system. When you change the filter, an air pocket can get locked in the housing, and water rushing through causes it to vibrate noisily against the plastic.
FIX Purge the air. Turn the filter to the "on" (filtered) position. Slowly turn on the cold water at the faucet to a medium flow. Let it run for a full 2-3 minutes. You should hear the sputtering and rattling decrease and then stop as the air is forced out. It might take a bit for the flow to steady completely.
IF THAT DIDN'T WORK Check that the filter cartridge is seated correctly and fully pushed down into the housing. A crooked or partially inserted cartridge can cause turbulent water flow. Also, ensure the housing is screwed on tightly and evenly—cross-threading can cause weird flow issues.
HEADS UP This is normal after a filter change and isn't harmful, but if the noise *starts* suddenly on an old filter, it could be a sign the internal components of the cartridge are breaking down. Time for a replacement.