B757 Captain reported applying aggressive braking to avoid another airplane during taxi. Flight continued for takeoff.

Narrative

On Day 0 at approximately XA:50; Flight ABCD had a taxi coordination issue at ZZZ Airport. Flight ABCD was delayed for departure at the gate due to a late arrival of the inbound aircraft. Before pushing back; the flight crew planned for a departure from Runway XXL from Taxiway 1. After pushback and taxi to Spot 1; Flight ABCD contacted ZZZ Ground Control and was cleared to taxi to Runway XYC at 2; via Taxiway 3; 4; cross Runway XYR; hold short of 5. After reviewing the taxi routing; the crew began taxiing toward Taxiway 3. As we approached Taxiway 3; an Airbus aircraft was observed on Taxiway 3 and entering our intended path. Ground Control did not issue instructions for either aircraft to give way. As the Airbus continued on Taxiway 3; I applied aggressive braking to avoid a potential conflict. Due to the abrupt braking; two flight attendants in the cabin were injured. The flight deck contacted the cabin immediately after the event to assess the flight attendants condition. Two flight attendants reported minor injuries but stated they were fit to continue the flight. We continued to the runway for an uneventful takeoff and flight to ZZZ1. Enroute; the crew asked Dispatch to have a Flight Attendant Supervisor meet the flight in ZZZ1.