The baryon mass content (i.e. stellar and gas mass) of dark matter halos in the early Universe depends on both global factors - e.g. ionizing ultraviolet (UV) radiation background - and local factors - e.g. star formation efficiency and assembly history. We use a lightweight semi-analytical model to investigate how both local and global factors impact the halo baryon mass content at redshifts of z ≥ 5. Our model incorporates a time delay between when stars form and when they produce feedback of 0 ≤ td/Myr ≤ 30, which can drive bursts of star formation, and a mass and redshift dependent UV background, which captures the influence of cosmological reionization on gas accretion onto halos. We use statistically representative halo assembly histories and assume that the cosmological gas accretion rate is proportional to the halo mass accretion rate. Delayed (td>0) feedback leads to oscillations in gas mass with cosmic time, behaviour that cannot be captured with instantaneous feedback (td=0). Highly efficient star formation drives stronger oscillations, while strong feedback impacts when oscillations occur; in contrast, inefficient star formation and weak feedback produce similar long-term behaviour to that observed in instantaneous feedback models. If the delayed feedback timescale is too long, a halo retains its gas reservoir but the feedback suppresses star formation. Our model predicts that lower mass systems (halo masses mh ≤ 107M⊙) at z ≤ 10 should be strongly gas deficient (mg → 0), whereas higher mass systems retain their gas reservoirs because they are sufficiently massive to continue accreting gas through cosmological reionization. Interestingly, in higher mass halos, the median m⋆/(m⋆ + mg) ≃ 0.01 – 0.05, but is a factor of 3-5 smaller when feedback is delayed. Our model does not include seed supermassive black hole feedback, which is necessary to explain massive quenched galaxies in the early Universe.