So why don't you believe this is not what it was like in the beginning?
Why would it be? Things change over time.
If DNA proves a common ancestry, why wouldn't original life have it?
Why would it? Why wouldn't DNA be the later development of a lineage of living things?
So if all life as we know it now has a common ancestor then I would extrapolate that the original life would have it too.
That would be an improper extrapolation. How does that follow logically, in your mind?
If DNA didn’t exist in the origins of life; how and when did we get a common ancestor?
What do these things have to do with each other? You need to refine your thought process before you post again.
Consider this simple model:
1) first living thing evolves with RNA-based genetics and enzymes.
2) decendants of that living thing develop DNA-based genetics and protein-based enzymes.
3) decendants of that living thing go on to evolve into all the living things that exist today.
Just because a group of living things share a quality, doesn't mean that every ancestor of those things shared the quality. Evolution is the source of novel structures in living things, and DNA at one point was one of those novel structures.