First postulated in 1931, the Big Bang has been the standard theory of the origin and structure of the universe for 50 years. In my opinion, (the opinion of a TV comedy writer, stripper and bar bouncer who does physics on the side) the Big Bang is about to collapse catastrophically, and that's a good thing.
According to Big Bang theory, the universe exploded into existence from basically nothing 13.7-something billion years ago. But we're at the beginning of a wave of discoveries of stuff that's older than 13.7 billion years.
For instance, there's SDSS J0100+2802, a quasar containing a black hole with a mass of 12 billion suns that's only 900 million years younger than the Big Bang. Black holes take a long time to accumulate mass, and 900 million years probably isn't enough. Astronomers have discovered more than 200,000 quasars, and with improving search techniques allowing them look closer and closer to the Big Bang, they'll find more of these highly developed quasars – the cosmic equivalent of 42-year-old strippers who are somehow only as old as toddlers when their ages are reckoned by the Big Bang.
Then we have dust made out of heavy elements in a galaxy that's only 700 million years younger than the Big Bang. Heavy elements form as stars near the ends of their life cycles, which are generally many billions of years long. So that's some fast-forming dust.
And the younger universe is wired like a humongous brain. A team led by scientists at UC Riverside has shown that the universe of seven billion years ago has a well-developed structure of large-scale filaments called "the cosmic web." Filaments ten billion years old and older have been found. Filaments are another feature of the universe which take time to form. As older and older filaments are found, they'll be harder and harder to explain in the context of the Big Bang.
The theory which replaces the Big Bang will treat the universe as an information processor. The universe is made of information and uses that information to define itself. Quantum mechanics and relativity pertain to the interactions of information, and the theory which finally unifies them will be information-based.
The Big Bang doesn't describe an information-processing universe. Information processors don't blow up after one calculation. You don't toss your smart phone after just one text. The real universe – a non-Big Bang universe – recycles itself in a series of little bangs, lighting up old, burned-out galaxies which function as memory as needed.
In rolling cycles of universal computation, old, collapsed, neutron-rich galaxies are lit up again, being hosed down by neutrinos (which have probably been channeled along cosmic filaments), turning some of their neutrons to protons, which provides fuel for stellar fusion. Each calculation takes a few tens of billions of years as newly lit-up galaxies burn their proton fuel in stars, sharing information and forming new associations in the active center of the universe before burning out again. This is ultra-deep time, with what looks like a Big Bang universe being only a long moment in a vast string of such moments across trillions or quadrillions of giga-years.
(The cosmological principle states that no observer has a favored location in the universe – that after a Big Bang, every point space looks roughly the same. But in a Big Bang, every point in time looks different as space blows up. In ultra-deep time, with a constant, long-ass series of little bangs, the universe looks roughly the same across Sagan's and deGrasse Tyson's billions and billions of years.)
Physics has been a little bit frozen – settled and established, tooling along in the behemoths of string theory and particle accelerators – for the past 30 years. The big thaw will come when the Big Bang falls.