Criterion for the Existence of the $G(3900)$ Resonance

About 18 years ago, the BABAR and the Belle Collaborations reported evidence for a new cc̄ structure near 3900~MeV in e⁺e⁻ → DD̄, triggering debate over whether it represents a genuine hadronic state or arises from interference effects and the opening of the D*D̄ threshold. The issue remained unsettled until 2024, when BESIII, with an enlarged e⁺e⁻ → DD̄ sample, confirmed the presence of the $G(3900)$ structure, reviving discussion of its nature. Although it has been proposed as a P-wave DD̄* molecular state, no consensus has emerged, and interference effects remain a plausible explanation. In this Letter, we show that analyzing the e⁺e⁻→ DD̄ cross section as a function of the transverse momentum of the final-state D meson reveals a prominent Jacobian peak. This feature cannot be generated by interference effects alone and thus provides direct evidence for the existence of $G(3900)$. Moreover, the peak position is highly sensitive to the actual mass of $G(3900)$, offering a precise determination method. Our results further disfavor the interpretation of $G(3900)$ as a DD̄* molecular state, pointing instead to alternative internal structures. The criterion illustrated by $G(3900)$ can be extended to other hadronic systems, offering a powerful tool to identify genuine resonances.