We can actually already see that time period, in its present form. It's called the Cosmic Microwave Background. It is the (now extremely cold) energy which permeated the entire universe in that very early time period. The entire universe was opaque and extremely hot... then as it expanded, it began to cool enough for particles and then atoms to form. Only then were stars possible, and later galaxies.

How/why can we see the CMB? Well, it was everywhere. Literally every point in the universe was a nearly uniform sea of blazing energy. So if you look far enough in any direction, you will see the cold echoes of that time period.

edit: Beat to the punch! I hope among our many answers you've found something enlightening

edit 2: Important to note that the CMB is not synonymous with the beginning of spacetime. It is more like a wall, beyond which we can't see anything, and it came down very early in time.