a. I had to publish those documents so that someone would believe me.
b. I had to publish those documents so that some people would believe me.
I think in (a) nobody believed me before I published those documents.
Is that correct?
And in (b) did anyone believe me before I published those documents?
Is it possible that some people did already believe me and the publication of the documents made some others believe me?
"Someone" can be used to refer to a person that you know but are not naming, for example, "I'm seeing someone" (to mean you are in the beginnings of a relationship with another person).
However, "someone" can also be used to refer to an unknown or not yet identified person, for example, "someone has stolen my wallet" (you don't know who), or "can someone help me?" (you are hoping someone will respond, but have no specific person in mind). It can also be used to refer to a speculative, or hypothetical person.
In your example (a) the action was taken without knowing who might believe it, so it is speculative. They can't possibly know that only one person would believe, so the "someone" does not necessarily represent just one person. Many people could come to believe them, but by saying "someone" it suggests that they would be satisfied with just one person as a minimum.
"Some people" is not a plural of "someone". It can only really refer to some specific people. For that reason, your example (b) sounds wrong to me. Who are these people?
A better way of saying, in a hopeful way, that more than one person would come to believe it would be:
I had to publish those documents so that others would believe me.
As you said, both of these statements (when written idiomatically) sound like nobody believed them before they took this action.
