Be X-ray binaries (BeXRBs) consist of rapidly rotating Be stars with neutron star (NS) companions accreting from the circumstellar emission disc. We compare the observed population of BeXRBs in the Small Magellanic Cloud (SMC) with simulated populations of BeXRB-like systems produced with the COMPAS population synthesis code. We focus on the apparently higher minimal mass of Be stars in BeXRBs than in the Be population at large. Assuming that BeXRBs experienced only dynamically stablemass transfer, theirmass distribution suggests that at least similar to 30 per cent of themass donated by the progenitor of the NS is typically accreted by the B-star companion. We expect these results to affect predictions for the population of double compact object mergers. A convolution of the simulated BeXRB population with the star formation history of the SMC shows that the excess of BeXRBs is most likely explained by this galaxy's burst of star formation similar to 20-40 Myr ago.