We present a first Lattice Quantum Chromodynamics (QCD) prediction for the electromagnetic form factors (EMFFs) of the pion and kaon up to very large momentum transfers, i.e., $Q^2\sim$ 10 and 28 GeV$^2$, respectively. Our calculations utilize Wilson-clover fermions within the $N_f=2+1$ Highly Improved Staggered Quark (HISQ) ensemble at the physical point. For pion, we employ a lattice spacing of $a=0.076$ fm, and for kaon, we use two spacings, $a=0.04$ and $0.076$ fm, to mitigate discretization effects. The renormalized results indicate a rapid increase in $Q^2F(Q^2)$ at lower $Q^2$ values, which then stabilize for both pion and kaon. Notably, our findings align well with existing experimental data, establishing a reliable QCD benchmark for future experimental analyses from JLab12, EicC, and EIC.