Is the resolve to fast one of the first ten days of Dhu al-Hijjah on the night preceding it considered a sufficient intention, given that the intention for supererogatory fasting can be made after Fajr?

It is not a condition to form the intention to fast a voluntary fast during the first ten days of Dhu al-Hijjah, nor at any other time, according to the majority of scholars. Forming the intention for a voluntary fast after dawn is sufficient, and the fast is valid with it.