No the Sun cannot come between Earth and moon because its stationary.
Any clear morning this week around 10 a.m. you can see the moon riding high in the western sky. Many people are surprised to see the moon in full daylight, yet it is a completely normal occurrence.
A very common misconception in astronomy is that the moon is directly opposite the sun in the sky. In fact, the moon is only in this position for a single instant in the whole lunar month: the exact time of full moon, when it is 180 degrees away from the sun. The rest of the month it can be anywhere from 0 to180 degrees away and, at least in theory, visible in the daytime sky.
At full moon, the moon is exactly opposite the sun. This means that the moon rises just as the sun is setting, and sets just as the sun is rising. This is also the only night in the month when a lunar eclipse can happen. Even so, eclipses normally happen only one full moon out of every six; the other times the Earth's shadow is either too high or too low to touch the moon.