In his ninth Christmas sermon, St. Augustin wrote that just like Mary gave birth to Christ, so could the Church give birth to Christians in baptism, and the Christian could give birth to Christ through confessing Christian faith.  
 

Proinde quia veritas et pax et justitia Christus est,   hunc fide concipite, operibus edite:   ut quod egit uterus Mariae in carne Christi, agat cor vestrum in lege Christi.   Quomodo autem non ad partum Virginis pertinetis, quando Christi membra estis?   Caput vestrum peperit Maria, vos Ecclesia.   Nam ipsa quoque et mater et virgo est:   mater visceribus charitatis,   virgo integritate fidei et pietatis.   Populos parit, sed unius membra sunt, cuius ipsa est corpus et conjux.

Christ is truth, peace and justice.   Concieve him in faith and give birth to him in your actions.   In this way, your heart will do in the Law of Christ what the womb of Mary did in the flesh of Christ.   The childbirth of Mary concerns you, because you are the body of Christ.   Mary gave birth to your head, the Church gave birth to you.   Also the Church is mother and virgin.   She is mother through love,  virgin through the integrity of her faith and her piety.   She gives birth to entire peoples in order to make them limbs of the head, whose body and bride she is.

 (Sermo 192,2, PL 38, 1012).  

In his eighth Christmas sermon, St. Augustin told the Christians to do in their soul what they admired in the flesh of Mary, i. e. concieve Christ. 
 
 

Quod miramini in carne Mariae, agite in penetralibus animae. Qui corde credit ad justitiam, concipit Christum; qui ore confitetur ad salutem (Rom 10,10), parit Christum.

Do in your soul what you admire in the flesh of Mary.   Through faith you concieve Christ,   and through confessing Christian faith (Rom 10:10), you give birth to Christ.

(Sermo 191,4, PL 38, 1011.) 

The recently excavated fifth century baptistery in San Lorenzo in Lucina offers an occasion to meditate on the rites of baptism, which was celebrated in this baptistery during the Vigils of Easter and Pentecost.  

The most particular feature of this baptistery is the rectangular lateral basin, which perhaps was used for the blessing of the water before the baptism. For this reason, we borrow a meditation from the Roman prayer for the blessing of the water for the baptism of Easter baptism in the Sacramentarium gelasianum antiquum, one of the most important sources of knowledge about the liturgy of Rome.  

This ancient baptismal prayer describes the fertility of the Holy Spirit and of the virginal womb of the Church. The prayer is  known to us from a ms. from around 750 but may have been written already in the fifth century. This text was perhaps recited in front of the rectangular basin, or in front of the circular one:  
  

Domine...fontem..baptismatis aperis toto orbe terrarum gentibus innovandis,    ut tuae maiestatis imperio sumat unigeniti tui gratiam de spiritu sancto.    Qui hanc aquam regenerandis hominibus praparatum archano sui luminis admixtione fecundet,    ut sanctificatione concepta ab immaculato divini fontis utero in novam renatam creaturam progenies caelestis emergat,    et quos aut sexus in corpore aut aetas discernit in tempore, omnis in una pareat gratia mater infantia.

O Lord, you open up the font for the renewal of all nations of the world that they may receive grace of your only Son by the Holy Spirit at the command of your majesty.   Let the Holy Spirit, by the hidden admixture of his light, give fruitfulness to this water prepared for the rebirth of humankind,   that, with sanctification concieved in it, a heavenly offspring may come forth from the virginal womb of the divine font,   and that grace may be a mother to people of every age and sex, who are born into a common infancy.

The text: The text in Liber sacramentorum Romanae aecclesiae ordinis anni circuli (Cod. Vat. Reg. lat. 316/Paris Bibl. Nat. 7193, 41/56) (Sacramentarium gelasianum), herausgegeben von L. C. Mohlberg, Roma 1960, 72-73.  
  

See also: Antoine Chavasse, Textes liturgiques de l'Église de Rome. Le cycle liturgique romain annuel selon le sacramentaire du Vaticanus Reginensis 316 (Sources liturgiques 2), Paris 1997. 

Would you like to know the exact date of Easter baptism in the any year after 325? Check the site "Calculation of the Ecclesiastical Calendar" by Marcos J. Montes. Enter a year after 325 CE and a script will calculate the day of the Easter in the Western and Eastern Traditions, the movable feasts, and other significant liturgical celebrations.