The first one to do it will win a prize.
The first one to do it wins a prize.
The first one to do it won a prize.
The infinitive in general does not refer to an occurrence of the action in real time; rather it refers to the action abstractly, outside of time. You can see from the examples above that the main verb can be future or past or present. So, the infinitive clause (in bold) is subject-oriented, telling us something about the subject.
Is there a mechanic in town who can repair a 1952 Ford?
--The man to do it is Bob. He knows a lot about old cars.
We can paraphrase this clause with a relative clause:
The man who can do it is Bob.
or with a prepositional phrase:
The man for the job is Bob.