I have heard that other companies had already submitted their documents.
こんにちは!
ご質問ありがとうございます。
ご質問について、いくつか言い方が考えられますが、例えば、
I have heard that other companies had already submitted their documents.
として、『他の会社はとっくに資料を提出していたと聞きました。』とするのはいかがでしょうか。
また、
I was told that I don't need to provide the documents anymore because they can't wait any longer. It seems that other companies promptly submitted their documents right after the meeting. Having such an attitude is important, isn't it?
とすると、ご質問にある内容を伝えられます。
参考になれば幸いです。