[verb て-form] + はじめて [verb て-form] + 初めて
てはじめて means "only after", "not until": the て-form of a verb plus はじめて, "for the first time". Until the first half happened, the second half had not – usually a realisation, with わかる, きづく気づく or しる知る.
The second half reports what came of it. It is never a request, an invitation or a plan.
These go beyond a single realisation in the past.
With ものだ at the end, or a plain non-past, the pattern states something that holds for anyone.
はじめて is the kana spelling of はじめて初めて, and both are common. It is never 始めて, which belongs to 始める, "begin".