All living things discovered to date contain a common molecule, which we call DNA, and acquire properties according to the sequence in this molecule. So, is it just a coincidence that all living things use DNA, or does it point to the existence of a common ancestor?
You are correct that it's pretty amazing that all living things discovered so far have DNA in common! Scientists do not think that this is just a coincidence, it actually lends a lot of support to the idea that you mentioned that every living organism on Earth shares a common ancestor. In biology we call this the theory of common descent.

In science, when we talk about a theory, we mean a well-supported explanation of some aspect of the natural world. These theories can have varying degrees of confidence, but once they make it to a theory, it is one of the best explanations we have. The theory of common descent is a super strong one in the field of evolutionary biology. It's all about how every creature on our planet evolved from this one single ancestor over billions of years.

So, as life kept evolving and branching out, the basic structure of DNA and the genetic code stayed the same across different species. But the specific sequences within the DNA changed, and that's how we ended up with so many different types of life forms! It's actually not just DNA that supports this idea, though. There are other similarities between living organisms, like the way they replicate, transcribe, and translate DNA and RNA. These processes are very similar across bacteria, archaea, and eukaryotes, which lends further confirmation of the idea of a single-celled common ancestor as it is what we would expect to see if that was the case.