At this point light and darkness existed at the same time. It is unclear if they were intermingled or not.
Genesis 1:4 KJV And God saw the light, that it was good: and God divided the light from the darkness.
In the above scripture God moved light and Darkness apart, but we do not know if they were something like twilight or if they were so to speak side by side.
As far as one side of the Earth being in light and the opposite side in darkness that is a function of sunlight, which did not exist until:
Genesis 1:14 through 19 KJV And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years: And let them be for lights in the firmament of the heaven to give light upon the earth: and it was so. And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also. And God set them in the firmament of the heaven to give light upon the earth, And to rule over the day and over the night, and to divide the light from the darkness: and God saw that it was good. And the evening and the morning were the fourth day.
In the above Scriptures we learn that this was the beginning of time. Time is the passage of cycles of daylight and darkness. That is actually the result of the rotation of the earth so that the sun is alternately shining on one side of the Earth or the other. Since this rotation is continuous and neither accelerates nor decelerates, at this point one cycle of day and night becomes one day consisting of twenty four hours. It is unclear if the periods of morning and evening referred to as the first three days was a literal twenty four hour cycle or not, but it would appear that God, who is invariably consistent, by declaring the first three cycles of morning and evening as days one through three would be consistent with other time periods referred to as the remaining four days, since the rotation of the Earth apparently began in;
Genesis 1:1 KJV In the beginning God created the heaven and the earth.
Although we are not told that the Earth began its rotation at this point nor are we told that the Earth began its orbit around the non existent sun in verse 1 it is only reasonable to believe that The Earth did in fact begin to rotate on its axis and begin an orbit around a non existent Sun, since that is the primary basis for time and there were three periods referred to as days.
Hope this helps.