Air carrier Captain reported not being notified prior to departure that dry ice was onboard.

Narrative

On initialization of the aircraft we received a planned DG of 33 Ibs of dry ice. Prior to pushback we received a final DG stating it was loaded onboard and we acknowledged it via ACARS. During push we received a new final DG saying we had no dry ice onboard. We tried asking the push crew what the status actually was of the dry ice; but they lost headset coms on push so we couldn't speak with them. We followed up with ZZZ operations to verify no DG was onboard and they confirmed this. We then again acknowledged via ACARS that we had no DG onboard.Immediately after takeoff and on initial climb we received an acars message and printer message saying we now have the 33 lbs of dry ice DG onboard along with a new final weights (100 lbs heavier ZFW than programmed from no DG final weights; same CG). We followed up again with ZZZ operations and they stated we actually did have the DG onboard and there was confusion between the person who loaded the DG and the push crew who closed out the weights. We followed up with another dangerous goods acknowledgement and dispatch also reached out with confirmation. The rest of the flight continued without incident.