Arise in the name of thy Lord, the God of Mercy, amidst the peoples of the earth, and seize thou the Cup of Life with the hands of confidence. First drink thou therefrom, and proffer it then to such as turn towards it amongst the peoples of all faiths.This quotation is similar to a well known passage from Baha'u'llah's writings about teaching: "Whoso ariseth among you to teach the Cause of his Lord, let him, before all else, teach his own self, that his speech may attract the hearts of them that hear him." Sharing Baha'u'llah's message with others is certainly a major aspect of this passage. But in addition, the imagery resembles the way the Sacrament of the Eucharist is conducted.
Baha'u'llah, Summons of the Lord of Hosts, 105, p. 56
As someone who has grown up familiar with the Roman Catholic Mass, it seems to me that Baha'u'llah is using the Sacrament of the Eucharist, the sharing of the Body and Blood of Jesus, as a metaphor for service to His Cause. To speak of the "the Cup of Life" in a Christian context inevitably leads the reader back to Jesus' Last Supper with the Apostles: Then he took a cup, gave thanks, and gave it to them, saying, "Drink from it, all of you, for this is my blood of the covenant, which will be shed on behalf of many for the forgiveness of sins. (Mt 26.27-8)
Each Mass, the priest re-enacts this consecration of the bread and the wine. After the consecration the priest is the first to drink from the cup. He then begins sharing the Eucharist with the congregation. This is consistent with Baha'u'llah's exhortation to "First drink thou therefrom, and proffer it then to such as turn towards it amongst the peoples of all faiths." Though, perhaps, it goes without saying that the Catholic Church does not open the Eucharist to the peoples of all faiths. Baha'u'llah has in mind a wider distribution of the Cup of Life.
Worth keeping in mind are the diverging ways Catholic Tradition and the Baha'i Writings understand how a soul comes in contact with the divine.
For Catholics, the central concept is incarnation; that human flesh became divine in the person of Jesus, and that the bread and wine become his Body and Blood in the Sacrament of the Eucharist. Through the eating and drinking of the Eucharist a person is joined to the spiritual body of the Church, whose head is Christ Jesus. Whoever eats my flesh and drinks my blood lives in me and I live in that person. (Jn 6.56) Receiving the Body and Blood of Christ brings a person in contact with the divine.
And for Baha'is, the central concept here is manifestation, that divine qualities, such as love, knowledge, and joy, are like rays of the sun, emanating from God and reflected upon the mirror of human hearts.
So, when the teachings of Baha'u'llah are shared with others, if those teachings take root, a process of spiritual transformation takes place by which a person becomes a fuller manifestation of the divine qualities. Here, exemplifying certain spiritual characteristics brings a soul in contact with the divine.
It seems to me, when Baha'u'llah writes "seize thou the Cup of Life," he is discussing the manifestation of divine qualities in our souls, using physical imagery Catholics would associate with the Sacrament of the Eucharist and the concept of incarnation undergirding it. Perhaps, we might say the cultivation of spiritual qualities occupies the place within the Baha'i Faith that the Eucharist has played within Catholicism.