We report on the charged-particle multiplicity dependence of net-proton cumulant ratios up to sixth order from s=200 GeV p+p collisions at the Relativistic Heavy Ion Collider (RHIC). The measured ratios C4/C2, C5/C1, and C6/C2 decrease with increased charged-particle multiplicity and rapidity acceptance. Neither the Skellam baselines nor PYTHIA8 calculations account for the observed multiplicity dependence. In addition, the ratios C5/C1 and C6/C2 approach negative values in the highest-multiplicity events, which implies that thermalized QCD matter may be formed in p+p collisions.