Air carrier Captain reported receiving a request to acknowledge dangerous goods (DG) after brake release.

Narrative

I was selected for a random screening upon arrival at the airport. I was given a very thorough and time-consuming search; and thus arrived at the aircraft about 20 minutes prior to pushback. The First Officer had to do all of the preflight prep in my absence. We were unable to get the takeoff data message and after some troubleshooting realized we had missed an incorrect flight number that was loaded in the FMC. It was some combination of 1 and 0; which is probably why we missed it; but not the correct [number]. After correcting this error we were able to get the takeoff message. Upon brake release; we immediately received a notification form warning. I queried the Tug Operator if they had loaded dangerous goods (DG) and he replied yes; so we sent a dangerous goods summary request and subsequently acknowledged the dangerous goods; dry ice.Technically we had released the brakes prior to acknowledging the DG; which is not in accordance with SOP. We did not push without the acknowledgment. The notification form warning states prior to aircraft movement; while the DG summary states prior to brake release; which is more conservative.