No, I can’t confirm most or all scholarships are given between the time you apply to a school and when you are accepted. There are some awarded in the summer, there are some awarded in the fall before most students even apply. Most big scholarships are awarded by the school itself, so most are given before /at the same time as acceptance.
I really think you are imagining scenarios that aren’t likely to happen - big outside scholarship, getting accepted into a school that is need aware (I didn’t realize you were international). You just have to deal with the situation you are in and if you apply before you get the big outside scholarship, and the school turns you down because your need is too high, that’s just how it is. You could ask for reconsideration.