Background: Anterior cruciate ligament (ACL) injuries in youth athletes are multifactorial, and the relative contributions of neuromuscular and neurocognitive variables remain inadequately comprehended. Methods: In this prospective cohort study, 220 young handball players (104 girls and 116 boys; mean age 16.3 ± 1.4 years) participated in functional testing with the Back in Action system and baseline neurocognitive evaluation with the ImPACT battery. During the 24-month follow-up period, orthopedic specialists identified ACL damage, which was confirmed by magnetic resonance imaging (MRI). Univariable logistic regression and receiver operating characteristic (ROC) curve analyses were conducted to evaluate predictive capability. Results: During the 24-month follow-up, 26 athletes sustained an ACL injury. Prolonged plyometric ground contact time was significantly associated with ACL injury occurrence in logistic regression analysis (p = 0.019) and demonstrated fair discriminatory ability (AUC = 0.63) (OR = 0.98 per ms; 0.98 95% CI: 0.964–0.997). Female sex emerged as a profound and independent risk factor (OR = 5.74). Conclusions: Neuromuscular performance, specifically plyometric ground contact time and female sex, has predictive ability for ACL damage in youth handball players, while separate cognition assessments failed to independently differentiate injury risk. These findings support the use of objective neuromuscular evaluation in comprehensive injury prevention strategies in youth sport.