Is it permissible to set a time for the prayer to be answered?

There is no harm in supplicating for an expedited provision, and the Prophet, may Allah bless him and grant him peace, supplicated for an immediate rainfall. However, it is better to entrust the matter to Allah regarding the timing of the response; for perhaps there is harm in an expedited response, or good in its delay, which opens the door to humility and increased reward.