You seem confused. There is no time restriction here. You could take a week or a day to reach rank 1. What I suggested is that perhaps you have to do it in uncer 50 games, for example, to qualify for qualification for the next league.
Perhaps we need a change to the rules where you can always reach rank 1 in each league, but you cannot enter the qualification for the next league unless you reach rank 1 in under a certain number of games. That would reset at the end of each sprint to always allow you to try again.