You're not going to find one answer on this. To some, the existence of God is self-evident, to others it's not. Then you get into "what does self-evident mean".
Some of those who say God is self-evident claim so because the complexity of creation screams "an intelligent designer made me". But that's not self-evident, it's evidence from creation.
Others claim Romans 1 and 2 - the existence of God is clearly known because He wrote it on our hearts, but that's not self-evident, either. The may point to 2 Peter chapter 3 as support that we know God, but are "willingly ignorant" because we'd rather walk after our own lusts, but that's not "self-evidence" either.
St. Thomas Aquinas addressed the question is his Summa Teologica, however, and gives a good answer (that also meets your requested criteria for a quote from a reputed theologian). emphasis mine in the passage below
He does an excellent job of defining what self-evidence is, and therefore showing how the existence of God meets (or doesn't meet) those definitions.
First Article
Whether the Existence of God Is Self-Evident?
We proceed thus to the First Article:—Objection 1. It seems that the
existence of God is self-evident. Now those things are said to be
self-evident to us the knowledge of which is naturally implanted in
us, as we can see in regard to first principles. But as Damascene says
(De Fid. Orth. i. 1, 3), the knowledge of God is naturally implanted
in all. Therefore the existence of God is self-evident.
Obj. 2. Further, those things are said to be self-evident which are
known as soon as the terms are known, which the Philosopher (1 Poster.
iii) says is true of the first principles of demonstration. Thus, when
the nature of a whole and of a part is known, it is at once recognized
that every whole is greater than its part. But as soon as the
signification of the word "God" is understood, it is at once seen that
God exists. For by this word is signified that thing than which
nothing greater can be conceived. But that which exists actually and
mentally is greater than that which exists only mentally. Therefore,
since as soon as the word "God" is understood it exists mentally, it
also follows that it exists actually. Therefore the proposition "God
exists" is self-evident.
**
Obj. 3. Further, the existence of truth is self-evident. For whoever
denies the existence of truth grants that truth does not exist: and,
if truth does not exist, then the proposition "Truth does not exist"
is true: and if there is anything true, there must be truth. But God
is truth itself: I am the way, the truth, and the life (John xiv. 6).
**Therefore "God exists" is self-evident.
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 (Ps. lii. 1). Therefore, that God exists is
not self-evident.
I answer that, A thing can be self-evident in either of two ways; on
the one hand, self-evident in itself, though not to us; on the other,
self-evident in itself, and to us. A proposition is self-evident
because the predicate is included in the essence of the subject, as
"Man is an animal," for animal is contained in the essence of man. If,
therefore the essence of the predicate and subject be known to all,
the proposition will be self-evident to all; as is clear with regard
to the first principles of demonstration, the terms of which are
common things that no one is ignorant of, such as being and non-being,
whole and part, and such like. If, however, there are some to whom the
essence of the predicate and subject is unknown, the proposition will
be self-evident in itself, but not to those who do not know the
meaning of the predicate and subject of the proposition. Therefore, it
happens, as Boethius says (Hebdom., the title of which is: "Whether
all that is, is good"), "that there are some mental concepts
self-evident only to the learned, as that incorporeal substances are
not in space." Therefore I say that this proposition, "God exists," of
itself is self-evident, for the predicate is the same as the subject;
because God is His own existence as will be hereafter shown (Q. 3, A.
4). Now because we do not know the essence of God, the proposition is
not self-evident to us; but needs to be, demonstrated by things that
are more known to us, though less known in their nature—namely, by
effects.
Reply Obj. 1. To know that God exists in a general and confused way is
implanted in us by nature, inasmuch as God is man's beatitude. For man
naturally desires happiness and what is naturally desired by man must
be naturally known to him. This, however, is not to know absolutely
that God exists; just as to know that someone is approaching is not
the same as to know that Peter is approaching, even though it is Peter
who is approaching; for many there are who imagine that man's perfect
good which is happiness, consists in riches, and others in pleasures,
and others in something else.
Reply Obj. 2. Perhaps not everyone who hears this word "God"
understands it to signify something than which nothing greater can be
thought, seeing that some have believed God to be a body. Yet, granted
that everyone understands that by this word "God" is signified
something than which nothing greater can be thought, nevertheless, it
does not therefore follow that he understands that what the word
signifies exists actually, but only that it exists mentally. Nor can
it be argued that it actually exists, unless it be admitted that there
actually exists something than which nothing greater can be thought;
and this precisely is not admitted by those who hold that God does not
exist.
Reply Obj. 3. The existence of truth in general is self-evident but
the existence of a Primal Truth is not self-evident to us.
