The correct option is A had started
Past perfect tense describes an action which is completed before a certain moment in the past. It is also used when two actions happened in the past, and one is linked to the other in terms of time. The simple past tense is used in one clause and the past perfect in the other.
In the given sentence, the clause, 'When I reached the theatre' is in simple past tense. The second clause should be in past perfect tense- its form being 'had' + past participle form of the verb (started). Hence, option A is correct.
Option B is in simple present tense. Option C is in simple future tense. Hence, these options are incorrect.
Option D: The phrase, 'to be started' is called a passive infinitive. It is used to indicate what is possible or what is correct. It cannot be used in the given blank as the action in the given sentence is in the past perfect tense.