I associate the term, 'properly basic belief', like Conifold, with Alvin Plantinga as its prime modern proponent. See for a start, see A. Plantinga, Warranted Christian Belief [WCB], Oxford: OUP, 2000: 81.
So that we can be quite clear what we are talking about, let's characterise the idea of a properly basic belief. We need to distinguish it from any belief elucidated or defended along the lines of classical foundationalism.
Conceptualising properly basic belief
What is the best way of understanding properly basic beliefs? One way is along
the lines of classical foundationalism, according to which a belief is properly basic if
and only if it is 'self-evident, incorrigible, or evident to the senses' (WCB, p. 84). Of
course, Plantinga forcefully argues that classical foundationalism is self-referentially
self-refuting, as the requirement that a belief must be either properly basic in the
sense just described or inferable from properly basic beliefs is itself neither properly
basic nor inferable from properly basic beliefs.5 He adopts a dif belief, one which is still foundationalist, but which (unlike classical foundationalism)
is fallibilist, admitting that basic beliefs are subject to defeat. ((Jeremy Randel Koons, 'Plantinga on Properly Basic Belief', The Philosophical Quarterly (1950-), Vol. 61, No. 245 (October 2011), pp. 839-850: 840.)
For Plantinga, a basic belief is essentially a foundational belief, a non-inferential
belief. Paradigm examples of basic beliefs are perceptual beliefs (as when one sees an
orange sphere and forms the belief 'There is a basketball') and memory beliefs (as
when one remembers 'I had a banana for breakfast'). In neither case is the belief
inferred from any other belief: it is immediate, non-inferential, basic. A belief is
properly basic if in addition to being basic, it is warranted for the individual.
Warrant, for Plantinga, is, of course, that which is added to true belief to produce
knowledge; it functions like justification and the Gettier condition in traditional
theories of knowledge. More precisely, a belief's warrant depends on the circumstances of the belief's production. For Plantinga, 'a belief has warrant for a person S
only if that belief is produced in S by cognitive faculties functioning properly (subject
to no dysfunction) in a cognitive environment that is appropriate for S's kind of
cognitive faculties, according to a design plan that is successfully aimed at truth'
(WCB, p. 156). (Because Plantinga uses 'justification' as a technical term distinct from
'warrant', I ... avoid the term 'justification' as a term for the
positive epistemic status of a belief; instead, I use 'warrant' to denote whatever is
added to a true belief to turn that belief into knowledge.) (Randell: 841.)
PLantinga's introduction of God into the picture
One could endorse this idea of a properly basic belief without any reference to God. Plantinga himself, as of course you know, links it with God. Just briefly to spell out how:
Plantinga argues that belief in God can, like perceptual or memory belief, be
properly basic. He thinks it likely that if there is a God, He wants us to know Him,
and has given us a way of knowing Him. Following Calvin, Plantinga postulates 'a
kind of faculty or a cognitive mechanism, what Calvin calls a sensus divinitatis or sense
of divinity, which in a wide variety of circumstances produces in us beliefs about
God' (WCB, p. 172). As this cognitive mechanism is designed to produce true beliefs
about God (and other conditions are or can be satisfied7), such beliefs about God (if
God exists) can be warranted, and we can indeed have knowledge of God, produced
by this sensus divinitatis. (Randell: 841.)