According to Catholicism, the Church Fathers and the Apostolic Fathers, Mary was the Mother of Jesus.
Archbishop Fulton Sheen is simply using the phrase "Mary is God's dream" in a devotional sense only. As such this phrase will not be read in the Apostolic Era or Church Fathers.
For them, Mary is not some sort dream of God, but a reality. The Church teaches that Mary was the Mother of Jesus. That is truth and not a dream!
Mary was a first-century BC Galilean Jewish woman of Nazareth, and the mother of Jesus, according to the New Testament and the Quaran.
The gospels of Matthew and Luke in the New Testament and the Quran describe Mary as a virgin. In Matthew and Luke she is betrothed to Joseph. According to Christian theology she conceived Jesus through the Holy Spirit while still a virgin. She accompanied Joseph to Bethlehem, where Jesus was born.
According to Catholic and Eastern Christian teachings, at the end of her earthly life her body was raised directly into Heaven; this is known in the Christian West as the Assumption.
Mary has been venerated since early Christianity, and is considered by millions to be the most meritorious saint of the religion. She is said to have miraculously appeared to believers many times over the centuries. The Eastern and Oriental Orthodox, Catholic, Anglican, and Lutheran churches believe that Mary, as mother of Jesus, is the Theotokos (Mother of God) (Greek: Θεοτόκος, romanized: Theotokos, lit. 'God-bearer'). There is significant diversity in the Marian beliefs and devotional practices of major Christian traditions. The Catholic Church holds distinctive Marian dogmas, namely her status as the Mother of God, her Immaculate Conception, her perpetual virginity, and her Assumption into heaven. Many Protestants minimize Mary's role within Christianity, basing their argument on the relative brevity of biblical references. Mary also has the highest position in Islam among all women. She is mentioned in the Quran more often than in the Bible, where two of the longer chapters of the Quran are devoted to her and her family. - Mary, mother of Jesus
The Catholic Church in particular holds the Mary is the Mother of Jesus and the Mother of the Church that was founded by her Son on the day of Pentecost. She is held in high esteem and is venerated as a saint. For the Church this is a reality and not some form of God’s dream! Mary is honoured with the devotional title of Mother of God.
In the Catholic Church, Mary is accorded the title "Blessed" (Latin: beata, Greek: μακάρια, romanized: makaria) in recognition of her assumption to Heaven and her capacity to intercede on behalf of those who pray to her. There is a difference between the usage of the term "blessed" as pertaining to Mary and its usage as pertaining to a beatified person. "Blessed" as a Marian title refers to her exalted state as being the greatest among the saints; for a person who has been declared beatified, on the other hand, "blessed" simply indicates that they may be venerated despite not being officially canonized. Catholic teachings make clear that Mary is not considered divine and prayers to her are not answered by her, but rather by God through her intercession. The four Catholic dogmas regarding Mary are: her status as Theotokos, or Mother of God; her perpetual virginity; her Immaculate Conception; and her bodily Assumption into heaven.
The Blessed Virgin Mary, the mother of Jesus has a more central role in Roman Catholic teachings and beliefs than in any other major Christian group. Not only do Roman Catholics have more theological doctrines and teachings that relate to Mary, but they have more festivals, prayers, devotional, and venerative practices than any other group. The Catechism of the Catholic Church states: "The Church's devotion to the Blessed Virgin is intrinsic to Christian worship."
For centuries, Catholics have performed acts of consecration and entrustment to Mary at personal, societal and regional levels. These acts may be directed to the Virgin herself, to the Immaculate Heart of Mary and to the Immaculate Conception. In Catholic teachings, consecration to Mary does not diminish or substitute the love of God, but enhances it, for all consecration is ultimately made to God.
Following the growth of Marian devotions in the 16th century, Catholic saints wrote books such as Glories of Mary and True Devotion to Mary that emphasized Marian veneration and taught that "the path to Jesus is through Mary". Marian devotions are at times linked to Christocentric devotions (e.g. the Alliance of the Hearts of Jesus and Mary).
Catholics place high emphasis on Mary's roles as protector and intercessor and the Catechism refers to Mary as "honored with the title 'Mother of God,' to whose protection the faithful fly in all their dangers and needs". Key Marian prayers include: Ave Maria, Alma Redemptoris Mater, Sub tuum praesidum, Ave maris stella, Regina caeli, Ave Regina caelorum and the Magnificat.
Mary's participation in the processes of salvation and redemption has also been emphasized in the Catholic tradition, but they are not doctrines. Pope John Paul II's 1987 encyclical Redemptoris Mater began with the sentence: "The Mother of the Redeemer has a precise place in the plan of salvation."
In the 20th century both popes John Paul II and Benedict XVI have emphasized the Marian focus of the Church. Cardinal Joseph Ratzinger (later Pope Benedict XVI) suggested a redirection of the whole Church towards the program of Pope John Paul II in order to ensure an authentic approach to Christology via a return to the "whole truth about Mary," writing:
"It is necessary to go back to Mary if we want to return to that 'truth about Jesus Christ,' 'truth about the Church' and 'truth about man.'" - Mary, mother of Jesus
Mary is definitely not some form of God’s dream, according to Catholicism, for on 1 November 1950, invoking his dogmatic authority, Pope Pius XII defined the the Assumption of Mary, the Mother of Jesus as dogma:
"By the authority of our Lord Jesus Christ, of the Blessed Apostles Peter and Paul, and by our own authority, we pronounce, declare, and define it to be a divinely revealed dogma: that the Immaculate Mother of God, the ever Virgin Mary, having completed the course of her earthly life, was assumed body and soul into heavenly glory". - Munificentissimus Deus
As a result of this solemn dogma being defined,
Pope Pius XII promulgated a new Mass for this occasion.
On November 1, 1950, Pope Pius XII infallibly proclaimed the dogma of the Assumption of the Blessed Virgin Mary. Of course, belief in Our Lady's Assumption into Heaven was nothing new, as testified by the 5th Glorious Mystery of the Rosary and a Mass in honor of her Assumption, titled Gaudeamus omnes.
To honor the declaration of the dogma, Pius XII commissioned a revised set of Mass propers for the feast (similarly as Pope Urban IV did for the Feast of Corpus Christi in 1264) which were introduced into the Missale Romanum in 1951.
Chief amongst the revisions was the composition of a beautiful new Introit by a Benedictine monk of Solesmes, starting with the words Signum magnum:
Signum magnum apparuit in caelo: mulier amicta sole, et luna sub pedibus ejus, et in capite ejus corona stellarum duodecim.
Cantate Domino canticum novum: quia mirabília fecit. Gloria Patri, etc.
A great sign appeared in heaven: a woman clothed with the sun, and the moon under her feet, and on her head a crown of twelve stars.
Sing ye to the Lord a new canticle: because He has done wonderful things. Glory be, etc. - Signum magnum: Mass of the Assumption
One can listen to the Introit of the Mass of the Assumption on this YouTube video: Sacred Chant from the Mass of the Assumption - Fontgombault.