Error Identification from TOEFL exam

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

‘To explore’ is correct. ‘The first person to do…something’. ‘Exploring’ does not fit the grammar, since the event is not currently underway.