  Lattice quantum chromodynamics (LQCD) calculations with physical pion mass
would revolutionize nuclear physics by enabling predictions based on the
fundamental theory of the strong force. To bridge the gap between finite-volume
LQCD results and free-space physical observables, two primary extrapolation
methods have been employed so far. The traditional approach relies on the
L\"{u}scher formula and its extensions, while a recent alternative employs
effective field theories (EFTs) fitted directly to the finite volume data. In
this study, we fit pionless EFT with perturbative inclusion of the
next-to-leading order to finite-volume energies generated from a
phenomenological $NN$ interaction. The theory is then used to extrapolate the
finite-volume results into free space as well as to predict new few-body
observables. As a benchmark, we also apply the L\"{u}scher formalism directly
to the finite-volume data. Through a comprehensive analysis, we explore the
characteristics of order-by-order predictions of the pionless EFT fitted within
a finite volume, investigate the limitations of the different extrapolation
techniques used, and derive recommended box sizes required for reliable
predictions.
