The relevant legislation provides:
he purchaser, or (if more than one) each of the purchasers, is a first-time buyer who intends to occupy the residential property as the purchaser’s only or main residence, and
Thus, if you satisfy this condition no SDLT is payable.
If, however, you have no intention of the property being your only or main residence SDLT is payable and you shouldn't have signed confirming it.
I am not aware that you need to move in on "Day One" to satisfy the condition; the test is one of intention.