Air carrier First Officer reported; after receiving the chocks in signal; they released brakes and the aircraft rolled backwards uncontrolled.

Narrative

At the conclusion of the flight to ZZZ airport; the aircraft was marshalled into and parked at the gate without issue in accordance with SOP procedures. The aircraft was subsequently shut down and both PF and PM performed their 'parking' flows. The PF then called for the parking checklist after viewing the 'chocks in' signal from the marshaller. I then read the checklist and the CA responded with the appropriate remarks. After the checklist was completed; aircraft secured at the gate; and flight deck door opened; one of the forward FA's was heard shouting 'stop; stop; stop.' After looking back into the cabin thinking it was likely a significant passenger disturbance; attention was then brought back into the cockpit where the jetbridge was seen in an abnormal position as viewed from the CA side DV window (Direct Vision window). With the gate agent at the control panel of the jetbridge just prior to it stopping movement; it was assumed the jet bridge had malfunctioned and began to retract uncommanded. Shortly after this transpired; one forward flight attendant came into the entryway of the flight deck and said 'they just broke the door; now we're stuck.' The CA then went into the forward galley and observed the situation while I remained in the flight deck. Throughout this event; there was never any attempt by the marshaller or the wing walkers to signal the flight crew of an issue with the aircraft or jetbridge such as uncommanded movement. After the event; the ground crew was observed all standing forward of the aircraft giving no signs of an issue. Upon consulting with the FA's; it was learned that approximately 4 passengers had already exited the aircraft prior to jetbridge/aircraft movement. Both forward FA's stated they felt the attaching of the jet bridge and subsequent opening of the MCD (Main Cabin Door) seemed abnormally fast and that the gate agent who opened the door seemed rushed. The lead flight attendant stated that they had not even completed their arrival procedures prior to the gate agent knocking on the MCD. I worked to confirm that no passengers or FAs were injured during the event. I also confirmed with the gate agent that none of the ramp personnel including themself were not injured and that none of the passengers who had disembarked the aircraft had fallen in the jetbridge during its possible movement.After completing the parking checklist; we had no internal or external indication of uncommanded aircraft movement. While discussing at a later time; the agent responsible for marshalling the aircraft stated that they never observed the aircraft rolling backward after giving the chocks in signal which was why they never signaled for the flight crew's attention. The gate agent who was operating the jet bridge had stated that the Marshaller was giving their wing walkers the 'chocks in' signal and not the flight crew and that they themselves had observed this while the jet bridge was attached. The Gate Agent then stated they would review footage with the airport to confirm and that the flight crew was forbidden from viewing the footage. They stated that they also shouted 'stop stop stop' from within the jetbridge which is confirmed by a forward flight attendant while they ran to the control panel in an effort to retract the jetbridge. Both wing walkers stated that they were actively placing the chocks when they noticed the aircraft moving and were not able to immediately chock the aircraft. They did not state if they had stopped the aircraft utilizing chocks or if the aircraft came to rest on its own.After informing Dispatch and Maintenance Control; a plan was made to deplane utilizing airstairs via door R1. This was done without issue. Airport operations; ARFF (Airport Rescue and Firefighting); and other personnel all greeted the aircraft but their assistance was not needed. We did suggest that they may need to carry a wheel chair passenger down the airstairs but the passenger ultimately decided to walkoff the aircraft. All passengers and bags were offloaded without further incident and the station was advised to not attempt to move the jetbridge until maintenance arrived. After reviewing the parking procedures in the SOP and the parking procedures in the Manual; and Bulletin; I believe there could be further emphasis placed on the verification of a secured aircraft prior to the attaching of the jetbridge and subsequent opening of the MCD (Main Cabin Door). The SOP states that the wingwalker is supposed to give the jet bridge driver a 'thumps up' allowing them to approach the aircraft with the jetbridge. It does not state whether this is before or after chocking the aircraft. On the line; it is also very rare to witness a wingwalker giving this signal.There also could be clarification on the signal used by the Marshaller to allow the wingwalkers to approach the MLG for chocking and the signal used to notify the flight deck that the chocks are in. Often time; complacency causes the signals to be nearly identical. Our procedures call for the release of the parking brake in the event that the brakes are over 350 degrees with the brake fans on; a frequent occurrence; especially in a fully loaded A320. Once we receive the chocks in signal; the brakes are to be released to prevent damage of brake components. Due to this procedure; it is prudent that the ground crew verify that the aircraft is secured utilizing chocks prior to giving the signal that they are placed.