In Reconfigurable Intelligent Surfaces (RIS), reflective elements (REs) are typically configured as a single array, but as RE numbers increase, this approach incurs high overhead for optimal configuration. Subarray grouping provides an effective tradeoff between performance and overhead. This paper studies RIS-aided massive random access (RA) at the Medium Access Control (MAC) layer in cellular networks to enhance throughput. We introduce an opportunistic scheduling scheme that integrates multi-round access requests, subarray grouping for efficient RIS link acquisition, and multi-user data transmission. To optimize access request timing, RIS estimation overhead and throughput, we propose a multi-user RA strategy using sequential decision optimization to maximize average system throughput. A low-complexity algorithm is also developed for practical implementation. Both theoretical analysis and numerical simulations demonstrate that the proposed strategy significantly outperforms the extremes of full-array grouping and element-wise grouping.