Do you mean what time was it in New York when the earthquake began ? OR Do you mean what time was it at the place where the earthquake occurred when the earthquake began ?
New York is in the Eastern Time Zone. That's five (5) zones west of UTC.
If the quake occurred between November and March, during the time when the US is on Standard time or "Winter" time, then the first P-wave was recorded in New York at 4:01 AM EST that morning.
If the quake occurred between April and October, during the time when the US is on Daylight Saving time or "Summer" time, when clocks are set 1 hour ahead, then the first P-wave was recorded there at 5:01 AM EDT that morning.
We have no way to calculate what the time was in the place where the earthquake occurred, because the question gives no information regarding the location of its epicenter. We would need to know not only its time zone, but also the actual distance from New York, so that we could estimate the length of time it took for the P-wave to reach the seismograph there.
