Air Carrier Pilot reported during pushback failing to set the brake resulting in the aircraft rolling forward until they were able to apply the brakes.

Narrative

While pushing back from the gate in ZZZ on flight to ZZZ1 I had a roll event. Pushing from this gate in ZZZ is a quick push where the aircraft doesn't travel very far. For that reason when we finished pushing the tug driver gave a clearance to set brakes and start engines at the same time. I thought this was out of the norm from how we receive clearances to set brakes and start engines. I looked over and prompted the FO to start the #2 engine. As the engine was spooling up I noticed the aircraft creep up a little bit. I set the brakes and no one was injured. The tow bar had already been removed from the aircraft. The tug driver queried why I hadn't set the brake. It was as much of a surprise to me as it was to them that it wasn't set. It could have been caused by the distraction of getting the two clearances at the same time; or it could have not engaged fully when setting it initially. No further disruption to the flight. Cause: I believe that it's easy to become distracted when getting non standard instructions from ground personnel. I received a set brake and cleared to start clearance at the same time. Ground personnel can ensure that these two clearances come at separate times. Flight crew can slow them down and get them to give both clearances separately.