This paper presents an innovative approach that leverages voice assistant systems (VAS) for the early diagnosis of cognitive decline. We developed Cog-TiPRO, a novel framework for detecting cognitive decline, by analyzing voice command data collected from 35 older adults (15 of whom interacted with the VAS daily) over 18 months. Cog-TiPRO combines linguistic feature extraction using LLM-based repeated prompt refinement, HuBERT-based acoustic feature extraction, and Transformer-based temporal modeling. Using iTransformer, we achieved 73.80% accuracy and 72.67% F1 score for Mild Cognitive Impairment (MCI) detection, a 27.13% improvement over existing methods. The LLM approach identified linguistic features that characterize the daily command usage patterns of individuals experiencing cognitive decline.