I really dont know what that means, but it seems to me that はじめて means to start something.
Unless the te form has something to do with it, I’m at a loss.
The only thing I can offer is to see the movie yourself so you can get the context.
It’s a movie that’s based in the era of WW2. It can be found on netflix.
I could give you more examples if that would help, but could it be that vocabulary differs more depending on dialect? Or perhaps it’s more like the difference between the American cigarette, and the way the British people call a cig?
て+いる is a form to describe an ongoing action, repeated action or a resultant state. In the case you mention, the いる has been inflected into past tense. So in your case it can mean something like “was started” or “was begun”. Is there more context to the phrase?
In this corner of the world… It can’t be found on Netflix.
You could watch it again and give us full phrases, dialogues and pictures, to provide us with more context. Otherwise you’ll have to wait to see if anybody has seen the movie on here and wants to discuss it more.
Edit: But it seems @athomasm actually knows how to find stuff on the internet, so you won’t have to wait after all!
初めて can mean ‘first time’. 始める means to begin something.
Yeah, looking through the subtitle file I see a couple of 初めて
子供だけで海渡るの 初めてじゃ
楽しいね
（すず）初めて見た
わしとすずさんが初めて会うたんは
この橋の上じゃった
and the only 始めて is this:
九一式五〇〇馬力から始めて
ここまできたかのう
I’m pretty sure based on what I can find that what you heard was actually ‘初めて見た’ which is completely different. Which would mean something literally like “Saw for the first time” or more naturally in English it could be “That’s new” when someone was looking up at something in the sky and have seen something they haven’t before.
This is also why using Japanese subtitles are helpful because then you can compare what you hear to what they are actually saying. It’s good for listening practice.