が早(はや)いか

が早(はや)いか is an expression in Japanese that groups with verbs, for the purpose of indicating an action which is immediately followed by a second, often unexpected action. It is a combination of the case-marking particle が, the い-Adjective 早(はや)い 'soon', and the adverbial particle か. It is often translated as 'no sooner than (A), (B)', or 'the instant that (A), (B)'. The more literal translation, taking into account the use of か, is '(A), or possibly sooner, (B)'. This just illustrates the instantaneousness of the (B) action in that (A) was unable to be determined as actually completed before (B) started.
This grammar pattern is formal, and will follow verbs in their dictionary or past tense forms. The verb that comes in the (B) phrase will always be in the past tense.

• 彼女(かのじょ)は彼(かれ)が書(か)いた手紙(てがみ)を読(よ)むが早(はや)いか、悲(かな)しさのあまりで泣(な)き始(はじ)めた。
  As soon as she read the letter from her boyfriend, she started to cry out of sadness.
• 息子(むすこ)は食卓(しょくたく)に座(すわ)るが早(はや)いか、並(なら)べてあった夕食(ゆうしょく)を吸(す)い込(こ)むように食(く)い上(あ)げた。
  As soon as my son sat at the dining table, he ate all the food that was out as if he sucked them up.
• 木村(きむら)くんはアラームが鳴(な)ったが早(はや)いか、スヌーズボタンを押(お)した。
  As soon as the alarm went off, Kimura-kun pressed the snooze button.
• 警察官(けいさつかん)は犯人(はんにん)を見(み)つけたが早(はや)いか、犯人(はんにん)に飛(と)びつき手錠(てじょう)をかけた。
  As soon as the police officer saw the suspect, he jumped onto him and handcuffed him.

(A) will tend to be actions that happen momentarily, or having a clearly defined finish point. For actions that don't have a clearly defined finish point, 終(お)わる 'to finish' will often be linked to the stem form, in order to specify the end. Additionally, while the (B) action will often be unexpected, it will also usually be volitional, that is to say something done intentionally.