Error Identification from TOEFL® exam

[Schwartz]

In a record dive in his bathysphere, William Beebe was the first person to explore the ocean at a deep of 3,028 feet.

correct answer : a deep ----> a depth

but I wonder, is 'to explore' correct? why not 'exploring'.

TOEFL listening lectures: A lecture from an American History class

[Mister Micawber]

'To explore' is correct. 'The first person to do...something'. 'Exploring' does not fit the grammar, since the event is not currently underway.
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Native English teacher at Mister Micawber's