Luke records Mary's faith on the occasion of the Annunciation (Luke 1:26-56). Gabriel informs her (v35) that "the child to be born will be holy; he will be called Son of God", and she replies (v38) "let it be done to me according to your word". When Elizabeth addresses her as "the mother of my Lord" (v43), Mary proclaims with the Magnificat (vv46-55), invoking her faith in "God my saviour", and her expectation of the fulfilment of God's promise. This would seem to demonstrate both knowledge and trust in the Messiah-hood of Jesus.
After the ascension of Jesus, Mary is recorded as praying together with the remaining apostles, in the upper room:
Then they returned to Jerusalem from the mount called Olivet, which is near Jerusalem, a sabbath day’s journey away. When they had entered the city, they went to the room upstairs where they were staying, Peter, and John, and James, and Andrew, Philip and Thomas, Bartholomew and Matthew, James son of Alphaeus, and Simon the Zealot, and Judas son of James. All these were constantly devoting themselves to prayer, together with certain women, including Mary the mother of Jesus, as well as his brothers. Acts 1:12-14
From this continuation of Luke's account, it is clear that Mary retained faith in Jesus following his resurrection. At this point, he's spent several weeks instructing the disciples, so she is participating in prayer with people who have seen and spoken with the risen Lord. She could not have been praying together with them, in this way, if she did not share in the same faith.
(All Biblical quotations are from the NRSV.)