Is it possible to distribute a database publicly?

As a pastime project, I have decided to work on practical way to verify the authenticity of digital data (derived from https://www.anf.es/pdf/Haber_Stornetta.pdf). I have decided to use git(http://blog.sysbase.org/the-blockchain-question/) as a mean for keeping all records up to date. However, I still have doubts about git's feasibility.

Is there a way to distribute an SQL database--for example--publicly and yet keep all versions up to date(asynchronously), similar to blockchain yet different?

I am aware of the existence of mirroring and replication, but it will require authorization. That wont do it, especially if my goal is to give access to anyone who wants it.