Each person must respond to the gospel in repentance and faith in order to become a Christian. But to label this "our act" or worse yet "our work" confuses things as if I labor and achieve something that I could not claim on my own. I appreciate how J. I. Packer addresses the subject:
"[The Bible] describes the initial conversion of unbelievers to God as the result of a divine work in them in which, by its very nature, they could play no part, since it is essentially a curing of the spiritual impotence which has precluded their turning to God hitherto: a raising from death (Eph. 2:1ff.), a new birth (Jn. 3:1ff.), an opening of the heart (Acts 16:14), an opening and enlightening of blinded eyes (2 Cor. 4:4-6), and the giving of an understanding (1 Jn. 5:20). Man responds to the gospel only because God has first worked in him in this way. Furthermore, the accounts of Paul's conversion and various references to the power and conviction imparted by the Spirit to the converting word (cf. Jn. 16:8; 1 Cor. 2:4f.; 1 Thes. 1:5) show that God draws men to himself under a strong, indeed overwhelming, sense of divine constraint."
I believe it is much more accurate to say conversion is man's repentant and trusting response to the gospel prompted and enabled by the Holy Spirit. So even as we make the wise choice of faith to ditch everything else to follow Jesus, all bragging rights still go to God.