The original Nick Valentine was Sole’s uncle.
The family had a long history in the law field and Nick’s sibling/Sole’s parent worked as a lawyer for the Commonwealth Institute of Technology before the bombs fell. As such they had a direct role in both advising their brother Nick to go for a “memory procedure” to see if it would help him cope with the loss of his fiancée and calling in favours from numerous people to ensure that their child and grandchild definitely made it safely to a vault.
As for synth Nick, when he first meets Sole he doesn’t quite remember where from but he can’t shake a distinct feeling of knowing them from somewhere before.
Or the odd little memory of a familiar looking child wearing a too big detective’s hat.