We cannot because light could not travel through the early universe. That took half a million years or so and the light from then has now redshifted into microwaves and has been imaged in great detail.
So if we saw something older than this thing (roughly), would that fundamentally disprove the Big Bang?
My understanding of the current state of the science is that there are many theories of the early state of the universe and early star formation but not a lot of definitive proof for any of it. However, the Big Bang is quite sound and as a rough theory has been well established since Hubble (the astronomer, not the namesake telescope) started measuring red shifts of galaxies. They actually have found stars that appear older than the universe, but the it's mostly believed that that's a problem with estimates of star age. All that said, there is plenty of research to be done from all angles.