In general no, it wasn't easy for poor folks to get their own farm land, and it became harder as time went on.
A plot of land was a common millitary pension; soldiers would retire there and work the land after putting in enough service time. This worked well while there was plenty of decent land in Italy, but became a worse deal over time. Once the prime land was taken up soldiers had to settle for plots of varying quality far from their homeland, which was much less pleasant as you'd expect.
The problem was the big farms relied virtually exclusively on slave labor for labor. There were numerous attempted reforms to require landowners to hire free citizens, but I don't recall about any systemic change being achieved before the fall.
> soldiers had to settle for plots of varying quality far from their homeland
So .. Mesopotamian soldiers might have to settle for land in Italy after serving at Arbeia [1], the Roman fort in England rather than return to their homeland?
Or are you perhaps thinking that the Roman Army was mostly made up of soldiers from provinces of what is now modern day Italy?
Things changed after the transition from Republic to an Empire. One of the factors in that transition was the shortage of land to provide to soldiers, who at that time were mostly Roman citizens.