The more natural choice is “unloaded on a future date” when you mean the action happens on a specific date, because on is used with exact dates. “At a future date” is also grammatical, but it sounds less specific and more formal or indefinite.

Usage

  • Use on with a particular day or date.
  • Use at with a time point, or when you mean “later/some time in the future” rather than a named date.

Better examples

  • The shipment will be unloaded on June 15.
  • The shipment will be unloaded at a later date.
  • The shipment will be unloaded on a future date if the date is already set.

Practical answer

If you are choosing between the two, “unloaded on a future date” is usually the better option for a written, natural-sounding sentence. “At a future date” is acceptable, but it feels more general and less precise.

TL;DR: Use “on a future date” for a specific date; use “at a future date” only if you mean vaguely later.