There is an empty room with a 1000 watt light bulb which is off
if someone turn on that light from outside the room,
there won't be any darkness in that room.
We don't have to conceive the light and the earth in Gen 1:3-5 that way. The historical survey of Young Earth positions by prominent early church fathers should broaden our horizon to many Biblical possibilities. This answer is based on Ken Ham's hypothesis described in my answer to your other question According to the Young Earth Creationism, how is the whole earth globe after the creation of the light?:
The first three days are written the same way as the next three. So if we let the language speak to us, all six days were ordinary earth days. . . . The sun is not needed for day and night. What is needed is light and a rotating earth. On the first day of creation, God made light (Genesis 1:3).
The phrase “evening and morning” certainly implies a rotating earth. Thus, if we have light from one direction, and a spinning earth, there can be day and night.
Source: Light Before the Sun: How biblical apologists have historically understood the source of light before the sun was created in Genesis 1
If we conceive the "light" in Gen 1:1-3 as temporary lighting of the earth placed similar to where our sun currently is (i.e. shining on earth from one direction) then it's quite straightforward to interpret Gen 1:4 as follows:
In Genesis 1:3–5, we are greeted with light. According to most commentators, the light was either created by God or manifested by himself. This light separated the darkness, was observed by God as being “good” and was called “day” while the darkness was called “night.” Together they made up the first evening and morning of day 1 of creation week.
For full details, please see my answer to your other question According to the Young Earth Creationism, what does it mean Genesis 1:14 and 18?