Lattice simulations are the only viable way to obtain ab-initio Quantum Chromodynamics (QCD) predictions for low energy nuclear physics. These calculations are done, however, in a finite box and therefore extrapolation is needed to get the free space results. Here we use nuclear Effective Field Theory (EFT), designed to provide a low energy description of QCD using baryonic degrees of freedom, to extrapolate the lattice results from finite to infinite volumes. To this end, we fit the EFT to the results calculated with nonphysical high quark masses and solve it with the stochastic variational method in both finite and infinite volumes. Moreover, we perform similar EFT calculations of the physical point and predict the finite-volume effects to be found in future Lattice QCD calculations for atomic nuclei with mass number $A\le4$.