We have recently suggested [1, 2] that Inflation could have started in a local minimum of the Higgs potential at field values of about 10(15) - 10(17) GeV, which exists for a narrow band of values of the top quark and Higgs masses and thus gives rise to a prediction on the Higgs mass to be in the range 123-129 GeV, together with a prediction on the the top mass and the cosmological tensor-to-scalar ratio r. Inflation can be achieved provided there is an additional degree of freedom which allows the transition to a radiation era. In  we had proposed such field to be a Brans-Dicke scalar. Here we present an alternative possibility with an additional subdominant scalar very weakly coupled to the Higgs, realizing an (inverted) hybrid Inflation scenario. Interestingly, we show that such model has an additional constraint m(H) <125.3 +/- 3(th), where 3(th) is the present theoretical uncertainty on the Standard Model RGEs. The tensor-to-scalar ratio has to be within the narrow range 10(-4) less than or similar to r <0.007, and values of the scalar spectral index compatible with the observed range can be obtained. Moreover, if we impose the model to have subplanckian field excursion, this selects a narrower range 10(-4) less than or similar to r <0.001 and an upper bound on the Higgs mass of about m(H) <124 +/- 3(th).