A testable prediction is a statement that is either proven true or proven false in a scientific experiment. It is also known as a hypothesis.
For an Atheist, it's simple: Evolutionary scientific theory has mountians of testible evidence and Design theory has no testible evidence or proof, just conjecture and usually unfounded conclusions that require "faith" (belief in a system without, or in contrary to, evidence). Keep in mind that scientific theory and the common useage of the word "theory" have two different definitions.
A hypothesis should be testable because it allows researchers to empirically evaluate its validity through experimentation or observation. Testability enables the collection of data that can confirm or refute the hypothesis, making it a fundamental aspect of the scientific method. This ensures that scientific claims are based on evidence and can be independently verified, fostering progress in knowledge and understanding.
To answer the question, an Atheist does not accept god claims due to lack of testible proof. There are no facts, just faith (belief in something without, or in spite of, proof) and conclusions without verifiable evidence. If there were varifiable evidence of a god, an atheist would have no choice but to accept there is a god claim as being factual and true.