We study the \(\Upsilon(1S)\) meson photoproduction on protons and nuclei at the near-threshold center-of-mass energies below 11.4 GeV (or at the corresponding photon laboratory energies \(E_{\gamma}\) below 68.8 GeV). We calculate the absolute excitation functions for the non-resonant and resonant photoproduction of \(\Upsilon(1S)\) mesons off protons at incident photon laboratory energies of 63--68 GeV by accounting for direct (\({\gamma}p \to {\Upsilon(1S)}p\)) and two-step (\({\gamma}p \to P^+_b(11080,11125,11130) \to {\Upsilon(1S)}p\)) \(\Upsilon(1S)\) production channels within different scenarios for the non-resonant total cross section of elementary reaction \({\gamma}p \to {\Upsilon(1S)}p\) and for branching ratios of the decays \(P^+_b(11080,11125,11130) \to {\Upsilon(1S)}p\). We also calculate an analogous functions for photoproduction of \(\Upsilon(1S)\) mesons on \(^{12}\)C and \(^{208}\)Pb target nuclei in the near-threshold center-of-mass beam energy region of 9.0--11.4 GeV by considering respective incoherent direct (\({\gamma}N \to {\Upsilon(1S)}N\)) and two-step (\({\gamma}p \to P^+_b(11080,11125,11130) \to {\Upsilon(1S)}p\), \({\gamma}n \to P^0_b(11080,11125,11130) \to {\Upsilon(1S)}n\)) \(\Upsilon(1S)\) production processes within a nuclear spectral function approach. We show that a detailed scan of the \(\Upsilon(1S)\) total photoproduction cross section on a proton and nuclear targets in the near-threshold energy region in future high-precision experiments at the proposed high-luminosity electron-ion colliders EIC and EicC in the U.S. and China should give a definite result for or against the existence of the non-strange hidden-bottom pentaquark states \(P_{bi}^+\) and \(P_{bi}^0\) (\(i=\)1, 2, 3) as well as clarify their decay rates.