space time - How was all the matter curled up inside a singularity during big bang ?

Ahh, yes, I suggest you watch this short video of mine on YouTube: https://www.youtube.com/watch?v=o-LbvFB33fw
I talk about the beginning of the Universe in it.
Basically, space and time didn't really exist at the time of the Big Bang. A single point in space is called a zero-dimensional entity because it has no length, no width, and no height, nor does it have any other dimensions.
SO no space. Also, since the Big Bang was the origin of time, you can't have anything "before" it.
SO no time.
And these two completely contradict your question itself: there was no spacetime. Nor was there any matter.

You see, Einstein once wrote on some black board in 1905 this very particular equation: E = mc^2

This stated that mass and energy are interchangeable. Mass requires space, but energy does not. Where all this points to is:

all the mass in the Universe was energy at the Big Bang, and since energy doesn't need space in order to exist, it was the Universe.

Also, the term "singularity", though used by many, isn't really the right word to call the original universe. But that's ok, as long as everyone knows what you're talking about.

To answer your question directly, there wasn't infinite mass in the beginning of the Universe; there was zero. There was a lot of temperature, but not infinite. And density . . . if the Universe had been infinitely dense, it would have been a black hole, and we wouldn't exist in any possible way. And there was no space-time to start with in the first place; space-time only became a later concept. A concept originating in the first 10^-35 of a second.