Elder John Clark, first generation leader in the anti mission movement, and of the newly formed "Old School" or "Primitive" Baptist denomination, was one in agreement with Elder John Watson in affirming that the Gospel was the means God employed in the regeneration of sinners, as I have shown previously. He started the famous periodical in the early 1850s called "Zion's Advocate." Here is another couple citations which show his thinking on this topic.
"And as that which is born of the flesh is flesh, and that which is born of the Spirit is spirit, and they that are in the flesh cannot please God, it follows, as a necessary consequence, that to please Him we must be born of the Spirit – born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth forever (1 Pet. i. 23). In this change, the faith, without which we cannot please God, is given, which is the fruit of the Spirit, and the vic tory that overcomes the world; and hence those who have faith are not in the flesh, but in the Spirit, for “Whosoever believeth that Jesus is the Christ, is born of God.” (1 John 1.)"
The "faith" that is given in regeneration is not the non cognitive faith that today's Hardshells describe as being given in regeneration because Elder Clark cites I John 5:1 which shows that it is evangelical faith that he has in mind. This faith involves "believing" that Jesus is the Christ.
Clark also said:
"The people of God were in Christ before the world was, according to that choice, and they are in him in time by faith – become children of God by faith in Christ; and hence, some are in Christ, in this sense, before others, as the apostle stated on a particular occasion. (Rom. xvi. 7.)" ("EXPOSURE OF HERESIES PROPAGATED BY SOME OLD SCHOOL BAPTISTS," CHAPTER SIXTH REGENERATION - see here)
Here Clark says, without equivocation, that sinners become the children of God by faith in Christ, just as Paul affirmed in Galatians 3: 26.