スター・トレック

私は先週に、現物の原作のスター・トレックを見始めましたる初めます。何が起こっているかを見るわかるためにそれを見て必要はありません。それはいいバックグラウンドノイズ環境ビデオです。

”初め”　and "始め" sound the same as "hajime".  But the meaning of kanji are different.

"初め" is used for the meaning in a situattion like  "for the first time" or "in the beggining of ...".

"始め” is used in case of "start something".

I knew the word "background noise" and Japanese don't use it in Japanese even by katakana.

I guess you would like to use it like "bacground music".  If so, there is a word "環境ビデオ(kankyo video)" in Japanese.  But actually we rarely use it in our daily life. 
I tried to keep your original text when I corrected it.  But if I said it in my way, I would say as "BGMみたいなものです。(it's almost like a BGM.)"
BGM is a word for music, but I won't use the word related "video" or "noise".

I hope that anyone could help you in a better way.

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I started watching the original Star Trek last week. I don't necessarily have to see it to understand what's happening. It's good background noise.

スター・トレック

私は先週に現物のスター・トレックを見る初めます。

→　私は先週、原作の「スター・トレック」を見始めました。

何が起こっているかわかるためにそれを見て必要はありません。

→　何が起こっているのかを理解するためにそれを見る必要はありません。

それはいいバックグラウンドノイズです。

→　？

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I started watching the original Star Trek last week. I don't necessarily have to see it to understand what's happening. It's good background noise.

Could you explain me when do you use "a background noise?"

If you teach me the nuance, I may be able to explain you in Japanese...