Explanation

No, sooner I reached home than it started to rain.

نہیں، میں گھر پہنچتے ہی بارش شروع ہو گئی۔

Sentence structure: No sooner + auxiliary + subject + main verb + than + subject + simple past 

'No sooner..than' is used to suggest that one action takes place immediately after another action.

When 'no sooner..than' is used at the beginning of the sentences then the auxiliary verb goes before the subject.

No sooner always introduces the event that occurred first.