You can't. White oak or the ashes of white oak can kill the ancestral family, because Esther linked them with ancient white oak when designing spells to gain immortal power, so white oak has the ability to seize this immortality.

On the other hand, Silas became an immortal even earlier. The spell they designed was more perfect, and the method of immortality was completely different from the "white oak method", so the white oak tree was invalid for him. Except that there is only one antidote, so far, the series has not revealed any way to break Silas' immortality. Even if there is, only Silas knows.

In fact, I personally think that there should be no way to kill Silas except knowing medicine. Because Kazija waited underground for so long, she created five brothers, gave them a task, made Silas drink the antidote and then killed him. Later, the boundary was broken, and the vampire hunter who came back from the dead was still looking for the antidote, which also proved from the side that if Silas wanted to die, there was only one way to let him drink the antidote.

At the end of the fourth season, Silas himself said that he could not die, so in order to balance, nature had to create a doppelganger for him, that is, a doppelganger. This further shows that his immortality is so perfect that even nature can do nothing.