Give some stream of consciousness and then the answer. The Convention approved the Committee's Electoral College proposal, with minor modifications, on September 6, 1787. Delegates from states with smaller populations or limited land area such as Connecticut, New Jersey, and Maryland generally favored the Electoral College with some consideration for states. At the compromise providing for a runoff among the top five candidates, the small states supposed that the House of Representatives with each state delegation casting one vote would decide most elections.

Answer this question: when did we start using the electoral college?
The relevant information is: The Convention approved the Committee's Electoral College proposal, with minor modifications, on September 6, 1787.
Therefore, the answer is September 6 , 1787.