The only way that this could ever happen would be if the man could prove that the child viewed the man as parent, and simultaneously prove that the mother was actually harming (abusing) the child. Even then, the court could decide to place the child in foster care, rather than with the man.
Visitation is a possibility, but again, the man would have to show a significant parent-child relationship, and it would still be an uphill battle.
Based on the way you describe the facts, I'd say the man's chances are effectively zero. But, no promises.
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