JavaScript (Node.js), 49 bytes

x=>~(g=s=>~s.search(x)||g(s+ ++i))(i='')+x.length

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-4 from Arnauld

Not using the 10

JavaScript (Node.js), 43 bytes

x=>~(g=s=>~s.indexOf(x,1)||g(s+i++))(x,i=1)

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Using range, fail 11 (expect 13, get 1)

JavaScript (Node.js) , 49 bytes

x=>~(g=s=>~s.search(x)||g(s+ ++i))(i='')+x.length

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-4 from Arnauld

Not using the 10

JavaScript (Node.js), 57 bytes

x=>(g=s=>(k=s.match(x))?k.index+x.length:g(s+ ++i))(i='')

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Not using the 10

JavaScript (Node.js), 49 bytes

x=>~(g=s=>~s.search(x)||g(s+ ++i))(i='')+x.length

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-4 from Arnauld

Not using the 10