Efficient container scaling is crucial for enhancing the availability and scalability of cloud-native applications through adaptive resource management. In cloud computing, the default autoscaling feature of Kubernetes scales pods only when the cluster or application exceeds a predefined threshold. However, this reactive approach often leads to significant resource waste during demand fluctuations because it cannot predict future workload changes and adjust resources in advance. This paper presents CATScaler, a novel Convolution-Augmented Transformer Scaler designed to proactively optimize resource allocation in serverless environments. CATScaler is a proactive approach composed of two modules: workload prediction and elastic auto-scaling. In the prediction module, we develop a convolution-augmented transformer to accurately predict workload changes at both local and global levels. Additionally, we incorporate reversible instance normalization to mitigate the shift caused by the difference between workload data and training data. In the auto-scaling module, we implement an instance-counting method to handle the nonlinear relationships between variables. Experiments using two real datasets from Alibaba Cloud and Huawei Cloud demonstrate the effectiveness of CATScaler. The tests conducted on a cluster of 4 servers demonstrated that CATScaler reduced response time latency by 1.1× compared to Kubernetes' default scaler and decreased service violation rates by 3.2×.