"To seek God" and "to attain God" is the goal of the Christian life.
Benedictines, when admitting a brother into their monastery, first "see whether he really seeketh God" (St. Benedict's Rule ch. 58).
Dom Marmion explains what seeking and possessing God means (Christ: The Ideal of the Monk ch. 1 "To Seek God"):
What does it mean to "seek" God?
Let us see what it is to seek God; […] if we truly seek God, nothing will prevent us from finding Him, and, in Him, we shall possess all good.
For us Christians, then, "to seek God", is to tend towards Him, not only as simple creatures who move towards the first principle and last end of their being, but supernaturally, that is to say as children who wish to remain united to their Father with all their strength of will urged by love, and through that mysterious participation in the very nature of God, of which St. Peter speaks [2 Pet. 1:4]; it is to have and to cultivate with the Divine Persons an intimacy so real and so profound, that St. John calls it, the “fellowship with the Father, and with His Son Jesus Christ,” in their common Spirit [1 Jn. 1:3].
It is to this the Psalmist alludes when he exhorts us to “seek the face of God” Quaerite faciem ejus semper [Ps. 104:4]: that is to say, to seek the friendship of God, to seek His love, as when the bride looking upon the bridegroom seeks to behold in his eyes the depth of his soul telling her of his tenderness. God is to us a Father full of goodness. He wills that even here below we should find our happiness in Him, in His ineffable perfections.
“To seek God", is to remain united to Him by faith, it is to attach ourselves to Him as the object of our love.
What does it mean to "find" God? How do we know we've found Him?
Another condition of the sincerity of our seeking is that it be exclusive. Let us seek God solely; I look upon this condition as capital.
Catherine of Sienna said on her death bed. […]
["Her first and fundamental principle":] that people who wish to begin to serve God must rid their hearts of all that kind of love into which the senses enter, not only for people but for any kind of creature whatsoever, and that they must seek for God the Creator single-mindedly and wholeheartedly. The heart, she said, cannot be entirely given to God unless it is delivered from all other affections and is simple and open and free from double-mindedness. [The Life of St. Catherine of Siena, Bl. Raymond of Capua, pt. 3 ch. 4]
It is to find God, “to please Him alone,” that, after the example of the great Patriarch, we have left all : Soli Deo placere desiderans ["Desiring to please God alone"], says St. Gregory [I Dialog. lib. II]. We must always remain in this fundamental disposition. It is only at this price that we shall find God. If, on the contrary, forgetting little by little our initial gift, we allow ourselves to turn aside from this supreme aim, if we cling to some person, some employment, some charge, some work or occupation, some object, then, let us be convinced of this, we shall never possess God fully.