Well, yea, a gift, but not a decision or a choice. A gift:
8 for by grace have ye been saved through faith; and that not of yourselves, it is the gift of God; Eph 2
It's a gift in the sense that it's fruit of the spiritual birth which absolutely must occur first:
7 `Thou mayest not wonder that I said to thee, It behoveth you to be born from above;
8 the Spirit where he willeth doth blow, and his voice thou dost hear, but thou hast not known whence he cometh, and whither he goeth; thus is every one who hath been born of the Spirit.` Jn 3
It's those whom God has wrought within that eventually come to the light:
20 for every one who is doing wicked things hateth the light, and doth not come unto the light, that his works may not be detected;
21 but he who is doing the truth doth come to the light, that his works may be manifested, that in God they are having been wrought.` Jn 3
I would think that even a 'milquetoast Calvinist' could understand the necessity of "regeneration before faith".