The story really starts when our protagonist is born into his third life (I mean, the title itself is "The Death Mage Who Doesn't Want a Fourth Time"). Before that, there are a couple chapters which set the stage, showing why Vandalieu is filled with thoughts of vengeance, why he knows death magic, and generally why he has a misfortunate existence. The catalyst for tension in his third life is the fact that he was born a dampir, a half-vampire, and society hunts and kills vampires and their offspring, so he must find a way to survive.
I think this manga is mainly interesting because of how absurdly young the protagonist is. If not for that quirk, he would just be another overpowered main character. That said, before he turns one year old, his character design looks stupid.
[Reviewed at chapter 13]