Is it theologically correct to say (as many believers do) that there are no coincidences?
YES, THEOLOGICALLY CORRECT TO SAY THAT THERE ARE NO COINCIDENCES.
“God takes care of the things of which
He is the cause.
And so,
the things that result from His action are subject to divine providence.
But we showed before that
God works through all secondary causes, and that all their products may be traced back to God as their cause; so it must be that the things that are done among singulars are
His works.
Therefore, these singulars, and also their motions and operations,
come under the scope of divine providence.
So, if God be only concerned with universals, and if He be entirely negligent of these singulars,
then His providence will be foolish and imperfect.
So, whatever a thing is, and whatever its mode of existing,
it falls under His providence.
Now, singulars are beings, and more so than universals,
for universals do not subsist of themselves, but are only in singulars.
Therefore, divine providence also applies to singulars.
Therefore, the participation of divine goodness by created things is accomplished by divine providence.
But even
contingent singulars participate in divine goodness.
So, divine providence
must extend even to them.
Hence it is said: “Are not two sparrows sold for a farthing: and not one of them shall fall on the ground without My Father” (Matt. 10:29; see 6:26)
By this conclusion
we set aside the opinion of those who said that divine providence does not extend as far as these singular things.”
https://isidore.co/aquinas/ContraGentiles3a.htm#
.
CATHOLIC ENCYCLOPEDIA Divine Providence
explains.
All things are created and governed
with a view to man, to the
development of his life and his intelligence, and to the satisfaction of his needs (Aristides, “Apol.”, i, v, vi, xv, xvi
.
His wisdom He so
orders all events within the universe that the end for which it was created may be
realized.
God preserves the universe in being;
He acts in and with every creature in each and all its activities.
He directs all,
even evil and sin itself, to the final end for which the universe was created.
Evil He converts into good (Genesis 1:20; cf. Psalm 90:10); and
suffering He uses as an instrument whereby to train men up as a father traineth up his children (Deuteronomy 8:1-6; Psalm 65:2-10;
Evil, therefore, ministers to God’s design (St. Gregory the Great, op. cit., VI, xxxii in “P.L.”,
http://www.newadvent.org/cathen/12510a.htm
.
We all should have the same faith in God then St.Thomas More had.
CCC 313 St.Thomas More, shortly before his martyrdom, consoled his daughter: “Nothing can come but that that God wills. And I make me very sure that whatsoever that be, seem it never so bad in sight,
it shall indeed be the best.” 182
.
CCC 324 Faith gives us the certainty that God would
not permit an evil if he did not cause a
good to come from that very evil, by ways that we shall fully know only in eternal life.
.
God bless