There is internal evidence in the book. Nahum told the Nineties to not be so overly secure, after all the city of Thebes feels safe surrounded by rivers and he will destroy it... so he spoke before the fall of Thebes.
Actually he spoke
after the fall of Thebes. Please read your Bible,
Are you better than Thebes
that sat by the Nile,
with water around her,
her rampart a sea,
water her wall?
9 Ethiopia was her strength,
Egypt too, and that without limit;
Put and the Libyans were her helpers.
10 Yet she became an exile,
she went into captivity;
even her infants were dashed in pieces
at the head of every street;
lots were cast for her nobles,
all her dignitaries were bound in fetters.
Clearly the author is writing after Thebes has fallen. That does not help much, does it?