Air carrier pilot reported while parked at the gate the aircraft rolled forward uncontrolled due to the parking brake not being set.

Narrative

During engine start sequence in ZZZ; the aircraft slowly rolled forward unexpectedly. Aircrew were notified immediately by mechanic through Intercommunication's Systems (ICS) and stopped the aircraft. No contact with any ground obstacle was noted although the mechanic did say it came toward his truck. When the mechanic alerted us to the rolling; his call to us was brake; brake; brake. In the cockpit we were thinking he was responding to an engine start anomaly and we quickly shut off the fuel for the engine being started. Then we quickly looked up (away from the EICAS) and noted the aircraft movement and applied the brakes. The mechanic then briefed us he was going to disconnect and take a look around. He came back and told us nothing seemed out of order and no contact was made with anything. We had a brief discussion of what we saw and let him know that his initial call drove us to think it was an engine start alert. We then started the engines and proceeded without incident. Causes; reasons. We did not know why the aircraft rolled. It could have been one of three reasons: the parking brake was inoperative; it was released unintentionally; or it was never set initially. We then tested the set parking brake and all seemed to work. We were unsure how it could have been released but it is a possibility. The most obvious answer was that it was never set initially. This actually would have been very unlikely in that in my Preflight Checklist procedures I physically grab the underside of the parking brake handle to ensure its in the right place; checking the light on as well. As a Captain I have repeatedly mentioned to newer First Officers that the Preflight Checklist is one where all the correct (or incorrect) responses can be read directly from the items being checked. Closed and locked; etc. Except for the Parking Brake handle; as when in the correct position. All it says is Parking Brake. For this reason I (we) have to do something else on that response. My technique is to grab the underside of the handle and ensure its up. I refer to the light on as well to ensure its on. I do look for something and not just at something. Learning. It is always imperative to ensure the checklists prevent mistakes and correct omissions in cockpit flows. In this case we did not know why the brake was released but will learn from this event to ensure it does not happen in the future.