“Alone” is only a connotation, since being 1 person is to be alone, right? It generally just means 1 person, but can be translated/interpreted through context.
Yeah, 一人 じゃありませんでした Literally means, “There wasn’t one person” but can change in context, e.g:
Sheepy: あたしは超悲しいひとですわ。 I am such a sad, sad person.
Everyone else: お前!一人じゃない! You’re not alone! 小さいOOがあるんだから!Your have your tiny ****!
Sheepy: 一人だけ来たの?今年寂しい誕生日ですね。。。何やってんだ、お母さん? Only 1 person came? This year is such a sad birthday… What are you even doing, mum?
お母さん: 一人じゃない!お父さんも。。。 Not just 1 person! Dad as well…
It’s all context, really. Like everything in Japanese.