💡 Detailed Explanation
The correct choice is 'そうになり' (from '〜そうになる' - to be on the verge of doing / almost do). The pattern '[Verb Stem] + そうになる' indicates that something almost happened but did not actually occur. Sentence translation: 'I slipped on the stairs and almost fell down.' 'はじめ' means started to fall, 'すぎ' means fell too much, which makes no sense here.