How big bang can store this huge amount of energy?

Let's think this thing through:
Big bang is implied by
Receding galaxies, which are implied by
Doppler shift, which is caused by
Motion away from us, which is assumed from
Red shifted light

So we have this remarkable train of logic all based on a single phenomenon and an assumption. If that assumption is wrong then most of what we think we know about the universe ain't so. Well, Doppler effect is not the only cause of red shift. Every hospital uses a magnet to produce a red shift. It's called MRI. But astronomers deny magnetic fields in space. So there you are: guesses offered in lieu of actual science.