For the first few hundred thousand years, the universe was opaque.
This link goes into a good amount of detail about the first light in the universe:
https://phys.org/news/2016-11-universe.html
We might be able to see a bit closer to the events after the Big Bang with a more powerful telescope in the future, but I don't think we can ever be able to actually "see" the Big Bang.
But there are other types of radiation that penetrate dense matter better: neutrinos and gravity waves. Right now it's "holy shit I saw one" for both kinds, so we're a long way off from doing any kind of imaging in those media. But if we ever manage detectors large enough and sensitive enough, we should be able to take "pictures" of the universe when it was even younger than when the CMB was released.
Dense enough matter will stop neutrinos, so that signal will be further back, but not the bang itself. So far as we know, nothing stops gravity--so that signal ought to be... interesting.
(Or at least, that's what Lee Smolin says in his book: Time Reborn)