The first scene in which Godzilla was seen in the 2014 movie was in Honolulu, with the second one occurring in San Francisco.
How much time within the movie passed between those two events?
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It's not clear as no times or dates are shown.
...we can estimate.
We know that Godzilla is first spotted some 50 miles from Hawaii and is then tracked and paced by the aircraft carrier and it's attendant ships.
The maximum cruising speed of such ships is around 40 nautical miles an hour (as an average) so let's use that as our basis.
In fact at one point it's mentioned that Godzilla is swimming at 33 knots and is picking up speed and will start to outrun the carrier.
However, let's stay with 40 mph for now...
The distance from Hawaii is roughly 2400 miles so that would translate to a journey time of around 60 hours (or 2.5 days).
Allowing for a fudge factor we can approximate a time of 3 - 4 days between the incidents.