The Vertical Pod Autoscaler (VPA) in Kubernetes automatically adjusts the CPU and memory requests and limits of the containers within a pod based on historical and real-time resource usage. In this scenario, where a single-replica stateful application needs more CPU during peak times, VPA can dynamically increase the CPU allocated to the pod when needed and potentially decrease it during off-peak periods to optimize resource utilization and cost efficiency.

Option A: Cluster autoscaling adds or removes nodes in your GKE cluster based on the resource requests of your pods. While it can help with overall cluster capacity, it oesn't directly address the need for more CPU for a specific pod.

Option C: Horizontal Pod Autoscaler (HPA) scales the number of pod replicas based on observed CPU utilization or other select metrics. Since the application can only have one replica, HPA is not suitable.

Option D: Node auto-provisioning is similar to cluster autoscaling, automatically creating and deleting node pools based on workload demands. It doesn't directly manage the resources of individual pods.

Reference to Google Cloud Certified - Associate Cloud Engineer Documents:

The functionality and use cases of the Vertical Pod Autoscaler (VPA) are detailed in the Google Kubernetes Engine documentation, specifically within the resource management and autoscaling sections. Understanding how VPA can dynamically adjust pod resources is relevant to the Associate Cloud Engineer certification.