[en] Superconductivity in Fe-based compounds is believed to appear due to magnetic spin fluctuations. Recent studies, however, revealed mysterious superconductivity with high transition temperature (Tc > 45 K) in CaFe₂As₂ under pressure and/or chemical substitution exhibiting collapsed tetragonal (cT) phase, which is believed to be non-magnetic. Here, we study the Fermiology of CaFe₂As₂ at different temperatures using Angle Resolved Photoemission (ARPES) spectroscopy. Fermi surfaces collected at different temperatures reveal the signature of three dimensional (3D) Fermi surface appearing at much lower temperature than the structural and magnetic phase transition temperature of 170 K. In addition, we discover energy bands not related to tetragonal/ orthorhombic CaFe₂As₂. These bands are distinctly resolved in the low temperatures high photon energy spectra from good quality sample and move away from the Fermi level with cooling. Experimental and theoretical analysis of the results attribute them to the cT phase hidden within the ambient structural phase presumably arising from the thermal compression induced strains. Thus, the hole pockets around the G-point gradually disappear with cooling leading to quantum fluctuations and absence of long range order at low temperatures. These results reveal the proximity of the material to quantum criticality causing exotic electronic properties. (author)