There are three phrasings in question
- a god
- the god (or the God)
The indefinite article (a god) is relevant to either a polytheist belief system (in which there is more than one god), a god independent of religion (as in comparing a god from one religion to a god from another, or to an ideal), or else somebody who is figuratively godlike (approaching perfection in a particular skill or knowledge, e.g. the top 50 users on this site are godlike).
Using a definite article (the god) is relevant to either a montheist belief system (in which there is just one god) or else somebody who is the definitive "best" (the most godlike) at a particular skill or knowledge, e.g. the #1 user on Stack Overflow (at this time of writing, #1 is 758k while #2 is 575k, so this is definitive). Capitalizing as the God refers to monotheism.
God without an article should always be capitalized. It refers to the god ahead of the speaker/writer's (monotheist) religion, particularly for Christianity and Judaism, both of which use "God" as one of their chief preferred proper names for that god.
Atheists tend to use a god, though may use the god or God as appropriate to whatever religion they are referring to. These lyrics are atheist. As they do not refer to any religions, they use the general case of a god.
When choosing a phrasing, be consistent. Assuming you're talking about a diety (rather than a person that is godlike), it is very important to always use the same format (within the same context). The song lyrics in question follow this advice.