QUIC, a new and increasingly used transport protocol, enhances TCP by providing better security, performance, and features like stream multiplexing. These features, however, also impose challenges for network middle-boxes that need to monitor and analyze web traffic. This paper proposes a novel solution for estimating the number of HTTP/3 responses in a given QUIC connection by an observer. This estimation reveals server behavior, client-server interactions, and data transmission efficiency, which is crucial for various applications such as designing a load balancing solution and detecting HTTP/3 flood attacks. The proposed scheme transforms QUIC connection traces into a sequence of images and trains machine learning (ML) models to predict the number of responses. Then, by aggregating images of a QUIC connection, an observer can estimate the total number of responses. As the problem is formulated as a discrete regression problem, we introduce a dedicated loss function. The proposed scheme is evaluated on a dataset of over seven million images, generated from $100,000$ traces collected from over $44,000$ websites over a four-month period, from various vantage points. The scheme achieves up to 97\% cumulative accuracy in both known and unknown web server settings and 92\% accuracy in estimating the total number of responses in unseen QUIC traces.