There was no sudden start, there was evolution throughout.
The basic logic is that God would create the universe with laws that would produce what he wanted without having to constantly create new things along the way. As Darwin put it:
In the same way, God created physical laws that creates rainclouds. He doesn’t need to create each and every raincloud because his laws are incapable of creating them.
I don’t see why they would believe that. God created nature with laws that would produce what he wanted, so if he doesn’t want something that is antibiblical then those laws would not produce them.