Choose the most appropriate option to fill in the given blank. By the time we…

Concept. When a sentence reports two events that both lie in the past, English can mark their order on the verb itself: the event that finished first takes the past perfect ('had' + past participle), while the event that fixes the later reference point stays in the simple past. 'By the time' is a standard trigger for this backshift - it names the later reference point, so the event completed before it is put into the past perfect, with 'already' placed between the auxiliary 'had' and the participle. With 'before' and 'after' the sequence is already carried by the linker itself, so the simple past is often acceptable there; 'by the time' is the construction that calls for the explicit backshift.

Application. In this sentence 'we arrived' is in the simple past, so the arrival is the later reference point. The beginning of the film happened before that arrival, so it has to be pushed one step further back in time into the past perfect: 'had already started'. The completed sentence reads 'By the time we arrived, the movie had already started.'

How the other verb forms would read:

• 'has already started' is present perfect, which ties a completed event to the present moment and therefore clashes with the past time frame that 'we arrived' has already set.

• 'have already been starting' is present perfect continuous, which describes an activity still running up to now, and its plural auxiliary 'have' does not agree with the singular subject 'the movie'.

• 'was already starting' is past continuous, which shows the beginning as unfolding at the moment of arrival instead of finished before it, so the ordering signalled by 'by the time' is lost.

Cross-check. Swap the linker: 'When we arrived, the movie had already started' preserves the same ordering, which confirms that the past perfect is what marks the earlier completion. Drop 'had' and that marking disappears from the verb, so the sentence leaves the ordering to be inferred instead of showing it - and that is why the formal 'by the time' construction takes the past perfect. Whenever one past event has to be shown as complete before another past event, the past perfect is the form that carries it.