No. The Universe was opaque to photons for the first 300,000 years. When the photons were released, they became the Cosmic Microwave Background, which is well observed.
In principle, there are other particles besides photons that started streaming free at earlier times --- the neutrinos in the thermal neutrino background, for example. Those particles could show the Big Bang at a time even earlier than the Cosmic Microwave Background. Dark matter may, in part, be such a particle.