Non-orthogonal multiple access (NOMA) is a key technology to enable massive machine type communications (mMTC) in 5G networks and beyond. In this paper, NOMA is applied to improve the random access efficiency in high-density spatially-distributed multi-cell wireless IoT networks, where IoT devices contend for accessing the shared wireless channel using an adaptive -persistent slotted Aloha protocol. To enable a capacity-optimal network, a novel formulation of random channel access management is proposed, in which the transmission probability of each IoT device is tuned to maximize the geometric mean of users’ expected capacity. It is shown that the network optimization objective is high dimensional and mathematically intractable, yet it admits favourable mathematical properties that enable the design of efficient data-driven algorithmic solutions which do not require a priori knowledge of the channel model or network topology. A centralized model-based algorithm and a scalable distributed model-free algorithm, are proposed to optimally tune the transmission probabilities of IoT devices and attain the maximum capacity. The convergence of the proposed algorithms to the optimal solution is further established based on convex optimization and game-theoretic analysis. Extensive simulations demonstrate the merits of the novel formulation and the efficacy of the proposed algorithms.