I thought you could give me time until I get the necessary document that I want to send to you.
"I thought you could give me time"＝「あなたは私に時間をくれると思いました」
"until I get the necessary document"＝「私が必要な書類を手に入れるまで」
(「書類が届くまで」という言い方で"get"の代わりに"receive"を使ってもOKです："until I receive the necessary document")
"that I want to send to you"=「あなたに送りたい書類を」
I thought you were ok waiting until I receive the documents I need.
I thought you didn't mind waiting for a bit until my documents arrive, so that I can complete my application.
ーI thought you were ok waiting until I receive the documents I need.
「必要な書類が届くまで待っていただけるはずだと思ったのですか。」
I thought you were ok waiting を使って「待ってもらえるはずだと思った」を表現できます。
ーI thought you didn't mind waiting for a bit until my documents arrive, so that I can complete my application.
「申し込みを終えれるよう、書類が届くまで少し待ってもらえると思ったのですが。」
don't mind waiting for a bit で「少しの間待つのは構わない」
complete one's application で「申し込み・申請を終える・完了する」
ご参考まで！
アメリカ合衆国 
カナダ 
