First thing to check---are the shutoff valves under the sink working? The cold one might not be fully on or is broken in the off position.
Next think to check---are the water feed lines twisted or kinked?
Did the soft copper lines on the faucet get crushed or twisted when the water lines were installed?
Shut off the hot water under the sink---then check the cold water shut off--look at hoses and faucet tubes.
Check the filter screen for debris---it's between the pullout head and the stainless steel hose.
Come back and tell us if this works---post a picture if you can.---Mike----