The private 5G-and-beyond networks have the ability to fulfill the high data rate, low latency, and massive connectivity requirements of industrial IoT (IIoT) automation. As a result, the slice selection requests arriving at the control plane functions (CPFs) of the private 5G-and-beyond networks will increase. The network has to scale up its resources to improve the response time for slice selection requests. The scaling up of resources will lead to an increase in operational expenditure (OPEX). We propose a novel approach to the slice selection method in private 5G-and-beyond networks for industrial IoT that improves response time for slice selection requests and reduces OPEX for the networks. The response time of our proposed method (protocol) for $u$ IIoT devices is approximately $\frac{1}{u}$ times that of the traditional slice selection protocol, and the number of instances of CPFs required for the proposed protocol is also lesser than that of the slice selection protocol in 5Gs networks.