We can! It’s the cosmic microwave background radiation which is the “light” from the early universe. If you understand how redshirting works, it’s pretty amazing we are around to observe this. The further away a galaxy is the more space has expanded between us and it which shifts its light to the longer wavelength of the light spectrum. The Big Bang’s light was white hot and everywhere, as time progressed the light from this has redshifted so far down the spectrum that it is now only observed in the microwave wavelength. In the future, as the universe continues to expand, it will shift so far down the spectrum that it won’t be detectable.

I may have some stuff wrong and I’m by no means an expert in this, but this is the best to my understanding of it.