Contact the first cousins you may strike lucky.
I had this happen this year.
On my DNA site a person came on as a distant cousin linking with myself and 4 others, all proven to be on my paternal branch. I wrote to the person welcoming them to the family. They wrote back stating they didn't understand. I wrote explaining about the 5 of us and that we were all related to the children of my 3rd gt grandparents, where and when born and stating she must belong to another child as she was equidistant to all of us. Reply was I don't understand. The person thought parents ancestors were mid European not British. I left it there as I felt something was wrong.
Six months later the person sent me a message and asked for help, through DNA they'd found a half sister known to them as a friend, also a half brother and a female 1st cousin, all in the same state in USA.
From the cousin the person was given the name of the lady's British grandfather. I was given the name and found his mother's maiden name was the same as mine and I even had mother on my tree. Mother's gt grandparent were my 3rd gt grandparents via one of their sons.
I was able to, in a couple of hours, give the person their family branch, dates, areas born and lived and occupations of ancestors. I am from that area so added a potted history of the area. She was very grateful to have everything sorted so quickly.
Remember it was the first cousin naming her grandfather (who turned out to be the person's father) that was the important fact, I just copied from my tree.
If you are lucky you may already have a first cousin of your father whose (gt) grandfather was your father's father.
If it's not you may need to be patient.
