The Vてはじめて、construction is generally taught as its own grammar point to mean "not until X", "only after X". However from what I've been told by other learners as well as natives, this is not a special construction with no special meaning and is instead simply just the て form of a verb followed by はじめて which then acts as an adverb on the next verb.
"only after I returned home did I realise that I lost my wallet" This follows the definition of はじめて given by weblio
I'm told though that it should be interpreted as
"I returned home and for the first time I realised I lost my wallet". Where はじめて is "linked" to 気がついた and not 帰る
The meaning in that second version is similar but not the same. "For the first time" vs "not until X". The emphasis in the former is on the realising while in the latter it's on the action of returning home and the subsequent change.
If this is correct that てはじめて is not a grammar point then the following questions arise,
- Does the position of はじめて matter in the meaning of the sentence?
- Why do dictionaries and resources present it as something different?
- How would you express the idea of "Not until X did Y happen"? the closest I can think of is てから