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Underwater wireless sensor networks (UWSNs) play a vital role in marine exploration and resource utilization. However, the unique characteristics of UWSNs pose significant challenges for designing effective medium access control (MAC) protocols. Especially, large-scale UWSNs present unique challenges due to limited propagation distances and long propagation delays. This article proposes a delay-aware and collision-free MAC protocol (DC-MAC) based on game theory. The protocol addresses access conflicts and improves throughput by a random handshake among multiple nodes. Modeling node behavior as a non-cooperative incomplete information game, a mixed transmission strategy is derived, allowing nodes to dynamically adjust their access probability based on the network size, reducing collision probability. Additionally, the concept of cluster head (CH) degree is introduced, considering the amount of CHs within a node's transmission range. Nodes with higher CH degrees experience more collisions and transmit data in advance. Moreover, the CH performs collision-free scheduling based on received data information, CH degree, and propagation delays. This enables collision-free data transmission among multiple nodes after a handshake cycle. The proposed DC-MAC protocol, rigorously assessed via simulations, substantiates its superior efficacy over extant protocols, achieving a 98% reduction in end-to-end latency and a 20% enhancement in packet delivery ratio (PDR).