時間がなくて

because I don't have time

→ 時間
phrase Rare #39,534
because I don't have time The て-form of 時間がない, used to connect the lack of time to a result or explanation. The subject can vary depending on context.
JA: 時間がなくて、今日は映画を見られません。
EN: I don't have time, so I can't watch a movie today.

時間がなくてたいへん困っている

I'm really struggling because I don't have enough time.

なにしろ時間がなくて

I just don't have any time, you know.

— 天空の城ラピュタ (1986)

私は午後は時間がなくて行けません

I don’t have time to go in the afternoon.

時間がなくて最終バスに間に合わない

I don't have enough time, so I won't make the last bus.