  We extend the prediction range of Pionless Effective Field Theory with an
analysis of the ground state of $^{16}$O in leading order. To renormalize the
theory, we use as input both experimental data and lattice QCD predictions of
nuclear observables, which probe the sensitivity of nuclei to increased quark
masses. The nuclear many-body Schr\"odinger equation is solved with the
Auxiliary Field Diffusion Monte Carlo method. For the first time in a nuclear
quantum Monte Carlo calculation, a linear optimization procedure, which allows
us to devise an accurate trial wave function with a large number of variational
parameters, is adopted. The method yields a binding energy of $^{4}$He which is
in good agreement with experiment at physical pion mass and with lattice
calculations at larger pion masses. At leading order we do not find any
evidence of a $^{16}$O state which is stable against breakup into four $^4$He,
although higher-order terms could bind $^{16}$O.
