how is it determined that this takes the 'Ki' concord for third person objects when there is no noun? Or is the 'Ki' concord the default in situations like this?
there's no way to know here. In context you would probably know what is starting and could use the concord of whatever it is. I would second @Gazelle1596 and say I usually default to "inaanza" for generic whatevers when they start.
I learned "Inaanza" with I- being the default; however I am sure Ki- is correct; but unfortunately I cannot explain the criteria/difference well.
When you say "it starts", your first thought might be "a thing starts", thus "ki", from "kitu".