I assume it's always a (vs)noun, so 開始三秒 must be a noun composed of 開始｛かいし｝ and 三秒｛さんびょう｝? If that is true, does it mean "before 3 seconds have elapsed?" (it would seem so from the context), but given that 開始 usually means something to do with beginnings I am probably wrong. This came up in this sentence:
As I understand it so far: "Within 3 seconds / before 3 seconds have elapsed [?] I beat the temptation to go back to bed again. I then check on my body in the mirror [without too much fuss]."