Yes, the moon can be in its first quarter phase on the Easter Sunday of a given year.
Easter falls on the first Sunday after the first full moon occurring on or after the vernal equinox. So, the phase of the moon during Easter will be a full moon.
First Quarter
The phase that comes before the last quarter is called the waning gibbous.
It is a point in the waxing gibbous phase and can also a point in the waning gibbous phase, but not in the first quarter.
New moon."New Moon" follows "waning crescent"New Moon
First Quarter
First quarter.
It takes about 7 days for the Moon to transition from a new moon phase to the first quarter moon phase.
First Quarter and/or Third Quarter.
7 days
7 days
The moon cycles through 4 phases every month. There are about 3 weeks between the first and last quarter phases of the moon.