Sayings about "the first one is the biggest sinner"

I can't think of a saying. In fact, there is an American (Western?) idea that each individual is responsible for their own behavior. If someone tries to reduce their culpability with "Susan did it first!", a common reply is "If Susan jumped off a bridge, would you do it, too?"

However, the word instigator often has a negative connotation, and that does sometimes contain the idea that the first person to do something is more blameworthy than followers:

instigate
verb tr.
1. To initiate or bring about, often by inciting: instigate a public discussion of the issue; instigate an uprising.

https://www.ahdictionary.com/word/search.html?q=instigator&submit.x=0&submit.y=0

instigator
noun
a person who causes something to happen, especially something bad: The instigators of the disturbance have not yet been identified.

http://dictionary.cambridge.org/dictionary/british/instigator

Finally, when trying to ameliorate fault or culpability, people might say He/she did it first, etc.

Words that come to mind for me are things like aggressor, instigator, and provoker.

Additionally, throwing the first stone in your example doesn't follow with the others, because that story hinges on the first person to throw stones being without sin.

The word ringleader combines the meanings 'instigator' and 'worst offender':

ringleader: The ringleaders in a quarrel, disturbance, or illegal activity are the people who started it and who cause most of the trouble.

{Collins Cobuild Reverso Dictionary}

I see in one of your comments that you really want 'the real "bad guy" [who] must be the one [insidiously] provoking the escalation of the situation'. That's an agent provocateur (looser sense):

agent provocateur

A [loan lexeme] meaning provoking agent, used to mean a person who deliberately encourages another to commit an illegal act for which they can be prosecuted.

{Dictionary of Unfamiliar Words by Diagram Group}