Epsilon-Near-Zero materials exhibit a transition in the real part of the dielectric permittivity from positive to negative value asa function of wavelength. Here we study metal-dielectric layered metamaterials in the homogenised regime (each layer hasstrongly subwavelength thickness) with zero real part of the permittivity in the near-infrared region. By optically pumping themetamaterial we experimentally show that close to the Epsilon-Near-Zero (ENZ) wavelength the permittivity exhibits a markedtransition from metallic (negative permittivity) to dielectric (positive permittivity) as a function of the optical power. Remarkably,this transition is linear as a function of pump power and occurs on time scales of the order of the 100 fs pump pulse thatneed not be tuned to a specific wavelength. The linearity of the permittivity increase allows us to express the response of themetamaterial in terms of a standard third order optical nonlinearity: this shows a clear inversion of the roles of the real andimaginary parts in crossing the ENZ wavelength, further supporting an optically induced change in the physical behaviour ofthe metamaterial.