When is it valid for a Muslim to make the intention for ablution (wudu')? Is it at the beginning, or when washing the face, or is it permissible at any time during the ablution?

Intention is a condition for the validity of ablution, without dispute. Its place is the heart, and it is not prescribed to utter it. The most complete way is for the intention to be at the beginning of the ablution or a short time before it, so that it encompasses all its parts. The obligation is for it to be with the first of the obligatory acts, and it is best to intend before washing the hands, so that the intention includes both the sunnah (recommended) and fard (obligatory) acts of purification.