Mystery of Life: How come DNA replicates itself, to allow cell mitosis and human body growth/repair?

The smallest living thing in our body is a cell, wich contains 23 pair of chromosome. Each one of them have a DNA molecule wrapped around a protein.

An adult man body typically contains 33 trillion cells, each one with 23 pairs of chromosome (one DNA molecule and a protein per chromosome). There are different types of cells, wich form the different organs and fluid of our organism.

DNA (the molecule of life) is based on a complex helical array of organic molecules, wich use only Hydrogen, Oxygen, Nitrogen, Carbon and Phosphorus. With these elements, large molecules that follow an specific pattern build up the DNA molecule.

Being that a DNA molecule has about 6 billion of nucleotides, each one averaging 34 atoms (Pyridimine rings, Pentose sugar, Phospate group), each DNA molecule has an average of 204 billion atoms.

Now, as you can see at this video, cells grow by mitosis. For this, each of the 23 pair of chromosome are DUPLICATED with UNKOWN MECHANISM.

The mechanism has to follow an EXACT ACCUMULATION of nucleotides, without FAILING, 6 billion times per replication.

Is anyone willing to negate that there is a Great Designer behind all of this?