If Aquinas were asked the question of the OP, he might have said, no, the belief in God is not properly basic, since although the belief that there is no God is not dependent on any other proposition, it can be rationally denied.

2+2=4.

Torturing babies for pleasure is morally wrong.

Aquinas is not so bad.

In pondering the behavior of our complex, law-abiding universe, it is as if we were watching a group of people running around randomly, and suddenly a baseball game emerges, with no one on the field conscious of the rules they are now playing under. And, just as in a baseball game, where we don’t see basketball games or soccer matches break out on the fringes of the field, the universe seems somehow to “hold together” and play by the same rules across its great expanse (or so it is assumed by science). Why should everything in the universe be subject to constant change except these immaterial laws—laws of physics, laws of chemistry? “There must,” says Roger Penrose, “be some underlying reason for the accord between mathematics and physics, i.e., between Plato’s world and the physical world." But no one—not scientists, not theologians—seems to have a clue as to why this should be so.

One Cosmos Under God: The Unification of Matter, Life, Mind, and Spirit, Robert W. Godwin

On the contrary, No one can mentally admit the opposite of what is self-evident; as the Philosopher (Metaph. iv, lect. vi) states concerning the first principles of demonstration. But the opposite of the proposition "God is" can be mentally admitted: "The fool said in his heart, There is no God" (Psalm 53:2). Therefore, that God exists is not self-evident.

http://www.newadvent.org/summa/1002.htm