Signal dimension, defined here as the number of copies with different delays or angular shifts, is a prerequisite for many high-resolution delay estimation and direction-finding algorithms in sensing and communication systems. Thus, correctly estimating signal dimension itself becomes crucial. In this paper, we present a deep learning-based signal dimension estimator (DLSDE) with single-snapshot observation in the example application of phased array radar. Unlike traditional model-based and existing deep learning-based signal dimension estimators relying on eigen-decomposition and information criterion, to which multiple data snapshots would be needed, the proposed DLSDE uses two-dimensional convolutional neural network (2D-CNN) to automatically develop features corresponding to the dimension of the received signal. Our study shows that DLSDE significantly outperforms traditional methods in terms of the successful detection rate and resolution. In a phased array radar with 32 antenna elements, DLSDE improves detection Signal to Noise Ratio (SNR) by >15dB and resolution by >1°. This makes the proposed method suitable for distinguishing multiple signals that are spatially correlated or have small angular separation. More importantly, our solution operates with a single snapshot signal, which is incompatible with other existing deep learning-based methods.