This is the 19732nd most frequent Korean word.
없으나
"없으나" means "though there is none" or "although it does not exist."
없으나 is used to contrast two conditions: lacking money and being happy.
그는 돈이 없으나 행복하다.
He has no money but is happy.
없으나 is used here to contrast the lack of time with the effort to prepare.
아침까지 시간이 없으나 최대한 준비했다.
I had no time until morning but prepared as much as possible.
없으나 connects the absence of issues with the advisability of rechecking the situation.