Formal English can drop if from a conditional and signal the same meaning through inversion instead. Had + subject + past participle replaces If the subject had...: Had we known about the delayed shipment sooner, the sales team could have warned the client in advance. This form is common in executive summaries and policy documents, where a formal, written tone matters. The main clause's could have still carries the third-conditional meaning; only the if-clause changes shape.

CORRECTED

The book's Checkpoint 25 keys the sentence "Never had the project been completed on time that the client was extremely satisfied" as correct inversion. It is not grammatical, and the two structures it borrows from do not combine this way.

Negative-adverbial inversion (never, rarely, no sooner) fronts the adverbial and inverts the auxiliary, but it does not license a following that-clause: Never had the project been completed on time is a complete, correct sentence on its own, with nothing more to add after it.

A that-clause of result needs its own correlate, so or such, earlier in the sentence: So complex was the system that only trained engineers could operate it. Such was the pressure from the stakeholders that the team had to work overtime for weeks. So pairs with a following adjective; such pairs with a following noun phrase. Neither so nor such appears in the book's own Checkpoint 25 sentence, so the that-clause has no correlate to attach to, and the sentence is both ungrammatical and illogical as written.