There was never one. Lot pleaded, but God never changed. God is omnipresent and simultaneously outside and all throughout time. He reveals that to us with his name: I AM.
He exists at all time...separating the beginning from end with a day like a thousand and a thousand years like a day. God knew all along that he would destroy Sodom and Gomorrah and it was for his glory that it was done.

That said...should we evangelize and engage in apologetics? Absolutely, because in doing so we get the privilege of being involved sharing the gospel with our brothers and sisters who have yet to wake from the delusions of this world...we also share with those who utterly reject the gospel and God is glorified in the rejection, and even persecution we face for doing so.