As for giving a month time, this is also part of the plan. Yes, it would give Kaiju time to refine the trident.
But a month is not enough to truly master a true divine artifact of a god. So, it is still not enough time for Kaiju to refine it. To refine such a weapon to truly become a master of it, it might take years, or decades or even hundred or thousands of years.
A month is not enough unless Kaiju got some divine luck, or some kid of method to facilitate the fast refining of such weapons which Azief doubt that Kaiju have.
As for the true reason why the time is given, it is so that the pirates, the criminals, the dark forces of the world could gather together.
Since Azief has already tear apart any face they had with each other, it means war.
And if it's a war, then at least Azief wanted to eradicate this threat completely.
If the world powers wins, the world would have a period of peace.