Answer:
To win
In this sentence it is used as a subject noun i.e. "To win the poetry contest" is acting as a subject noun.
Step-by-step explanation:
Verbal is a word made from a verb and used as something else in a sentence. e.g. gerund, participle adjective etc.
Infinitive: An infinitive is a type of verbal that can function as a noun, adjective or a verb.
Uses of Infinitive:
Infinitive can function;
As Noun (subject or object) e.g.
He likes to swim (as object).
To win the poetry contest would be exciting (as subject).
As Adjective e.g.
He had some work to do (modifies and explains work).
A good novel to read is War and Peace (modifies novel).
As Adverb e.g.
He worked hard to succeed in the examinations (tells why he worked hard).