Gamma decays were observed in $^{56}$Ca and $^{58}$Ca following quasi-free one-proton knockout reactions from $^{57,59}$Sc beams at ≈200 MeV/nucleon. For $^{56}$Ca, a γ ray transition was measured to be 1456(12) keV, while for $^{58}$Ca an indication for a transition was observed at 1115(34) keV. Both transitions were tentatively assigned as the $2_1^{+}\to 0_{\mathrm{gs}}^{+}$ decays, and were compared to results from ab initio and conventional shell-model approaches. A shell-model calculation in a wide model space with a marginally modified effective nucleon-nucleon interaction depicts excellent agreement with experiment for $2_1^{+}$ level energies, two-neutron separation energies, and reaction cross sections, corroborating the formation of a new nuclear shell above the N = 34 shell. Its constituents, the $0f_{5/2}$ and $0g_{9/2}$ orbitals, are almost degenerate. This degeneracy precludes the possibility for a doubly magic $^{60}$Ca and potentially drives the dripline of Ca isotopes to $^{70}$Ca or even beyond.