Essentially, without going into technicalities, a full-moon rises at the same time the sun sets. So a full-moon always rises at the same time the sun sets, or within a few minutes either way. That’s why it’s a full moon, because it’s facing the sun directly and therefore the moon will be rising in the East and the Sun will be setting in the West.
Sun set times change, as you know. Some times of the year, winter for example, the sun sets earlier and rises later, so we have shorter days. In the late spring early summer the sun sets later and rises earlier, so the days are longer.
But the full moon rises at sunset. There are some technical issues, like when exactly is the Moon full, but I’m just giving you the simple answer. As the full moon continues to rise the sky will grow darker because the sun already went down.
In this image the full moon rose, but was concealed by a hill. The photographer caught this shot as it rose above the hill and the sky was already darkening.