Neutrinos are known to pass though the Earth's atmosphere and even the Earth, itself (and anything standing, sitting, or laying on the Earth). However, I think most radiation left over from the Big Bang is deflected away from Earth by it's magnetic field. That's not to say that the Earth is radiation free. There is plenty of radioactive material within the Earth and we wouldn't survive long without the abundance of solar radiation given by our Sun.
“A new study using data from NASA's Chandra X-ray Observatory and Hubble Space Telescope gives new insight into an important question: how habitable are planets that orbit the most common type of stars in the Galaxy? The target of the new study, as reported in our press release, is Barnard's Star, which is one of the closest stars to Earth at a distance of just 6 light years. Barnard's Star is a red dwarf, a small star that slowly burns through its fuel supply and can last much longer than medium-sized stars like our Sun. It is about 10 billion years old, making it twice the age of the Sun…The research team's Chandra observations of Barnard's Star taken in June 2019 uncovered one X-ray flare (shown in the inset box) and their Hubble observations taken in March 2019 revealed two ultraviolet high-energy flares (shown in an additional graphic). Both observations were about seven hours long and both plots show X-ray or ultraviolet brightness extending down to zero. Based on the length of the flares and of the observations, the authors concluded that Barnard's Star unleashes potentially destructive flares about 25% of the time. The team then studied what these results mean for rocky planets orbiting in the habitable zone—where liquid water could exist on their surface—around an old red dwarf like Barnard's Star. Any atmosphere formed early in the life of a habitable-zone planet was likely to have been eroded away by high-energy radiation from the star during its volatile youth..."
Comments in post #2 "There is plenty of radioactive material within the Earth and we wouldn't survive long without the abundance of solar radiation given by our Sun." I feel need a good astronomical context like the Barnard star report cited.
It took ~ 380,000 years from the BB event before light could travel in one direction — meaning towards us, Before that time, light travelled only very tiny distances before scattering in wild directions; think herding a million cats in a very large field. The temperature of space kept electrons bouncing around freely. Once the expansion finally was great enough to get the temp down to ~ 3000K, then the electrons suddenly all combined (orbits) with protons. This allowed light to take off and we see it today as the CMBR. The expansion has caused that light’s wavelength to now be in microwaves.
There seems to be hope that a future neutrino detector might someday allow us to see much earlier moments.