Unbelievers, as well as certain apologetic schools, say it's question-begging to cite the Bible as evidence for God's existence. Here's a book by two philosophers challenging that widespread assumption:
The Agnostic Inquirer: Revelation from a Philosophical Standpoint by Sandra Menssen and Thomas D. Sullivan. Grand Rapids, MI: Eerdmans, 2007.
Sandra Menssen and Thomas D. Sullivan provide a straight- forward defense of using revelation to defend belief in God’s existence...Menssen and Sullivan specifically target what they call the “tacit assumption” of philosophy, namely, that one must show that God exists before one can ask whether God has revealed.
The tacit assumption is that a claim to have received a revelation can be evaluated only after the existence of God has been proved. In opposition to the tacit assumption, they make the following claim: If it is not highly unlikely that God exists, then it is reasonable to examine particular claims to revelation from God as evidence for God’s existence. It is not highly unlikely that God exists; therefore, it is reasonable to examine particular revelation claims as evidence for God’s existence. More boldly, they contend that if the existence of God is not highly unlikely, then a reasonable inquirer must actually examine a number of revelation claims before a judgment can be made that God does not exist.
Consider, they say, the proposal that a single person named Homer was responsible for the Iliad. In the course of history, many have rejected that possibility because it was believed that no preliterate person, such as Homer, could have composed such a work. Given the complexity and length of the poem, the argument reasoned, a single individual could have produced it only if that person had the capacity to write. If it were impossible for a preliterate person to produce the poem, no amount of contrary evidence internal to the poem would raise the likelihood that a single person produced it. In other words, the probability of an impossibility is zero and any evidence added to an impossibility does not improve the odds.
Suppose, however, that it were possible for a single individual, in a preliterate context, to produce such a long and complex poem. The probabilities change, and evidence for authorship does matter. Once such a possibility is recognized, then internal evidence derived from the content of the poem itself becomes relevant for judgments about authorship.
Menssen and Sullivan take revelation claims to be closely analogous to arguments about the production of the Iliad. If the possibility of God’s existence were nil, or next to nil, then no appeal to the internal content of revelation could support belief in the existence of God. On the other hand, if it is not highly unlikely that God exists, then just as it is relevant to look at the content of the Iliad to determine authorship, so is it reasonable to look at revelation claims for evidence of God’s existence.