'Hajimete' can be 1: 初めて(adverb) 2: 始めて(a variation of the verb 始める). In case of 2:, the URL that Kylecito mentioned will be useful. In case of 1:, the meaning is a) for the first time 第一次 b) only if(only after) ~~才 a) 私は初めて日本に来ました。 watashi wa hajimete nihon ni kimashita. I came to Japan for the first time. 我第一次来日本。 b) 病気になって初めて健康の重要性がわかりました。 byouki ni natte hajimete kenkou no juuyousei ga wakarimashita. I realized the importance of health only after I got sick. 我生了病才知道健康多么宝贵。

Hey there! I asked something pretty similar to this before, along with other questions http://www.italki.com/answers/question/31444.htm Hoping it helps