There has recently been a sharp increase in interest in Artificial Intelligence-Generated Content (AIGC). Despite this, musical components such as time signatures have not been studied sufficiently to form an algorithmic determination approach for new compositions, especially lyrical songs. This is likely because of the neglect of musical details, which is critical for constructing a robust framework. Specifically, time signatures establish the fundamental rhythmic structure for almost all aspects of a song, including the phrases and notes. In this paper, we propose a novel approach that only uses lyrics as input to automatically generate a fitting time signature for lyrical songs and uncover the latent rhythmic structure utilizing explainable machine learning models. In particular, we devise multiple methods that are associated with discovering lyrical patterns and creating new features that simultaneously contain lyrical, rhythmic, and statistical information. In this approach, the best of our experimental results reveal a 97.6% F1 score and a 0.996 Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC) score. In conclusion, our research directly generates time signatures from lyrics automatically for new scores utilizing machine learning, which is an innovative idea that approaches an understudied component of musicology and therefore contributes significantly to the future of Artificial Intelligence (AI) music generation.