Yes, justification is received with genuine human faith. But listen to Bavinck:
If for insignificant, guilty, and impure persons there is to be a possibility of true religion, that is, of genuine fellowship with God, of salvation and eternal life, then God on his part must reestablish the broken bond, again take them into fellowship with him and share his grace with them, regardless of their guilt and corruption.
He, then, must descend from the height of his majesty, seek us out and come to us, take away our guilt and again open the way to his fatherly heart. If God were to wait until we . . . had made ourselves worthy, in part or in whole, to receive his favor, the restoration of communion between him and ourselves would never happen, and salvation would forever be out of reach for us.
–Herman Bavinck, Reformed Dogmatics, 4:204-5