Is it permissible to change the intention from a fard (obligatory) prayer to a sunnah (supererogatory) prayer upon realizing that the time for the fard prayer has not yet begun?

Changing the intention from one specific prayer to another specific prayer does not validate either of them. However, changing the intention from a specific prayer to an absolute supererogatory (nafl) prayer does validate the prayer as a supererogatory one. So, if someone begins a fard (obligatory) prayer and then realizes that the prayer time has not yet begun, or realizes this after completing it, the prayer is valid as an absolute supererogatory prayer.

As for someone who begins the Fajr obligatory prayer and wishes to change their intention to the Fajr Sunnah (definition) (ratibah) prayer, neither the Fajr obligatory prayer nor its Sunnah prayer will be valid.

It is permissible to convert an obligatory prayer into an absolute supererogatory prayer for a valid reason, such as catching the congregational prayer, and this is preferable. However, it is disliked without a valid reason.

It is better not to do this to avoid scholarly disagreement, as many scholars prohibit interrupting an obligatory prayer after beginning it unless there is a necessity. Moreover, the Fajr Sunnah prayer can be performed after the obligatory prayer or after sunrise.