You likely connected the hoses backward.
Shut off the cold water valve. Check the connections. The existing cold water line from your house plumbing must connect to the filter outlet port. The outlet port is on the top cap. The included 3/8" braided hose must connect the cold water shutoff valve to the filter inlet port on the bottom cap.
Reverse them if they're wrong. Hand-tighten, then give a wrench an additional half-turn (or one full turn for plastic tubing). Do not over-tighten.
If connections are correct and still no water, the valve might not be fully open or there's a kink in the line. Ensure the unit is mounted vertically. Slowly reopen the shutoff valve a quarter turn at a time.
If water still won't flow, stop. Call APEC Water support at (800) 880-4808. Do not force anything.