If the density of the matter from which the first generation stars were made was homogeneous, so during the star formation nuclear fusion would have started around when they all reached to same critical mass and core temperature, once fusion started the outward pressure would have counteracted on inflow of matter so all stars should have been of similar size
If the universe had been entirely homogeneous then no stars would have formed. Star formation requires regions of over-density to collapse.
There are plenty of ideas of what determines the spectrum of masses that stars are born with (known as the initial mass function) - mainly concerning turbulence, fragmentation and accretion. The commencement of nuclear fusion is not a factor, since nothing really changes at the surface of a star when this happens (the luminosity is the same).
The reasons for the observed initial mass function in the present-day universe (which is remarkably similar from place to place) are not fully understood, so unsurprisingly, neither is it a settled matter in the early universe where it cannot even be observed. However, it seems likely on theoretical grounds that stars formed from pristine, primordial gas could be much more massive and less susceptible to fragmentation into smaller objects. Even if this is the case, simulations still suggest that stars would be born with masses that vary by orders of magnitude (e.g. Stacy (2016) and recent references therein).