My old school grammar says:
A to-infinitive follows after the first/the last, the only, the few and after superlatives.
The infinitive expresses what has happened or will happen. The infinitive stands for a relative clause.
Unfortunatately I have no idea why English in theses cases prefers the infinitive construction instead of a relative clause. Of course, the infinitive is a little bit shorter but I think a relative clause is acceptable, too.
Examples
1 We were the first to enter (= who entered) the exhibition that day and
2 the last to leave.
3 You are not the only person to have been there (= who has been there).
4 This is the biggest exhibition to have taken place here since 1938.
Source: Grundzüge der englischen Grammatik, Klett Verlag, 1972.