Why can't the Hubble telescope capture images of the start of the universe?

The universe is roughly 13.2 billion light years old and the latest images capture a galaxy 480 million light years after the big bang, so…how is it that we can see roughly 12.7 billion years into the past, but can’t see into the last few hundred million years? Will it eventually happen? When will we capture the first few images of the big bang? If ever.