The first is more nonsensical than the second
'She believes God' may be not sufficient and need to be complemented such as 'She believes (that) God must be a handsome man'
And the second has no need to be complemented. Its meaning is too easy-to-understand.
I just had another thought. If instead of replacing god with another being as I did in my last example (She believes Fred), we replace God with a theory (She believes in evolution) then the second one would be correct.
In summery, if the original poster believes in God as a being then both are correct, if the original poster believes that God is only a theory then only the second one is correct.