Background/Objectives: Non-obstructive azoospermia (NOA) is a severe form of male infertility characterized by the absence of sperm in the ejaculate due to impaired spermatogenesis. Testicular sperm extraction (TESE) combined with intracytoplasmic sperm injection is the primary treatment, but success rates are unpredictable, causing significant emotional and financial burdens. Traditional clinical and hormonal predictors have shown inconsistent reliability. This review aims to evaluate current and emerging non-invasive preoperative predictors of successful sperm retrieval in men with NOA, highlighting promising biomarkers and their potential clinical applications. Methods: A comprehensive literature review was conducted, examining studies on clinical and hormonal factors, imaging techniques, molecular biology biomarkers, and genetic testing related to TESE outcomes in NOA patients. The potential role of artificial intelligence and machine learning in enhancing predictive models was also explored. Results: Traditional predictors such as patient age, body mass index, infertility duration, testicular volume, and serum hormone levels (follicle-stimulating hormone, luteinizing hormone, inhibin B) have limited predictive value for TESE success. Emerging non-invasive biomarkers—including anti-Müllerian hormone levels, inhibin B to anti-Müllerian hormone ratio, specific microRNAs, long non-coding RNAs, circular RNAs, and germ-cell-specific proteins like TEX101—show promise in predicting successful sperm retrieval. Advanced imaging techniques like high-frequency ultrasound and functional magnetic resonance imaging offer potential but require further validation. Integrating molecular biomarkers with artificial intelligence and machine learning algorithms may enhance predictive accuracy. Conclusions: Predicting TESE outcomes in men with NOA remains challenging using conventional clinical and hormonal parameters. Emerging non-invasive biomarkers offer significant potential to improve predictive models but require validation through large-scale studies. Incorporating artificial intelligence and machine learning could further refine predictive accuracy, aiding clinical decision-making and improving patient counseling and treatment strategies in NOA.