why does it have the indefinite article [a] in the beginning?
Answer from a Native speaker
"A" is used in the beginning as it marks the beginning of the count, and since there's only one count-in before they begin, 'a' works well to mark 'one,' similar to how one might say 'a hundred' to mean 'one hundred.' The group of numbers kind of act as a singular countable noun referencing the count-in for the dance. Ex: On a one, two, three, four, spin and clap your hands. Ex: We'll start the song on a five, six, seven, eight.