Mexico City is the location with the largest number of boxers in Mexico; in fact, it is the first city in the country to open a Technological Baccalaureate in Education and Sports Promotion with a pugilism orientation. This cross-sectional study aimed to determine the physical–functional profile of applicants for admission to the baccalaureate in sports. A total of 227 young athletes (44F; 183M; 15.65 (1.79) years; 63.66 (14.98) kg; >3 years of boxing experience) participated in this study. Body mass (BM), maximal isometric handgrip (HG) strength, the height of the countermovement jump (CMJ), the velocity of straight boxing punches (PV), and the rear hand punch impact force (PIF) were measured. The young boxers were profiled using unsupervised machine learning algorithms, and the probability of superiority (ρ) was calculated as the effect size of the differences. K-Medoids clustering resulted in two sex-independent significantly different groups: Profile 1 (n = 118) and Profile 2 (n = 109). Except for BM, Profile 2 was statistically higher (p < 0.001) with a clear distinction in terms of superiority on PIF (ρ = 0.118), the PIF-to-BM ratio (ρ = 0.017), the PIF-to-HG ratio (ρ = 0.079) and the PIF-to-BM+HG ratio (ρ = 0.008). In general, strength levels explained most of the data variation; therefore, it is reasonable to recommend the implementation of tests aimed at assessing the levels of isometric and applied strength in boxing gestures. The identification of these physical–functional profiles might help to differentiate training programs during sports specialization of young boxing athletes.