The Bible has nothing direct to say on this subject, since the phrase did not become popular till the 19th Century.
The best known version of the phrase, “The greatest trick the Devil ever pulled was convincing the world he didn’t exist”, is a line delivered by the actor Kevin Spacey in the 1995 film The Usual Suspects, but similar phrases occur in earlier English sources. Many of these probably have their origin in the work of the French poet Charles Baudelaire. His collection Le Spleen de Paris (1869) includes Le Joueur généreux‘, a prose poem in which the Devil tells a gambler how he heard a preacher tell his congregation “la plus belle des ruses du diable est de vous persuader qu’il n’existe pas!”. Whether Baudelaire really believed this or was poking fun at the clergy of his time is debatable.
In contrast the Bible’s starting point with Satan is found in two Old Testament books – the prologue of Job and the vision in Zechariah 3 – is allegory, not literal and the allegory continues into the New Testament with around seventy verses, none of them giving any factual historical information about a rebel angel. So the question of whether this allegory can trick the world into being convinced that the allegory does not exist does not arise.
However there are verses in the Bible where sin is personified and Sin tricks and deceives :
“For sin, seizing an opportunity in the commandment, deceived me and through it killed me.” (Romans 7:11)
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