Just to add to previous answers.

For clarity, Sleep is a physiological phenomenon,

"characterized by altered consciousness, relatively inhibited sensory activity, inhibition of nearly all voluntary muscles, and reduced interactions with surroundings." - https://en.wikipedia.org/wiki/Sleep

While it's a subject of ongoing research, sleep is generally associated with the need to rest, with being tired, a direct association with being material and mortal.

As stated, God is not human, He is immaterial and eternal (Revelation 1:8, John 4:24). The idea of God sleeping doesn't make sense. Similar to asking if a bachelor can be married.

The example given above with Elijah:

At noon Elijah began to make fun of them. “Pray louder!” he said. “If Baal really is a god, maybe he is thinking, or busy, or traveling! Maybe he is sleeping so you will have to wake him!” (1 Kings 18:27, NCV)

Elijah is not just making fun of his opponents god's failure to act. He is, in a sense, charging them with not being real god's (or not even being real at all!).

It is helpful to compare Genesis 1.1-2.3 to other Ancient Near Eastern (ANE) creation texts; the meaning of God 'resting' can be determined by verbal cues and literary parallels to other ANE creation accounts.

John H. Walton notes that Enuma Elish – after Tiamat is slain, after the functions of the world are established from her remains, after humanity has been created – concludes with the creation of a temple for the god Marduk: 'Below the firmament, whose grounding I have made firm, A house I shall build, let it be the abode of my pleasure. Within it I shall establish its holy place, I shall appoint my holy chambers, I shall establish my kingship' (5.121-124). Later, 'We will make a shrine, whose name will be a byword, your chamber that shall be our stopping place, we shall find rest therein' (6.51-52).

The climax of the creation of the world was the creation of a temple, which would serve as the place of 'rest' for the supreme god-king Marduk.

Genesis 2.2-3 describes day 7. At this point, 'the heavens and the earth were finished' already, so day 7 is not an act of creating anything. Instead, day 7 gives meaning to what has just been created: God comes to 'rest'. Appealing to other Hebrew texts, Walton states that 'divine rest' in ANE thought always occurs in a temple. One key text that substantiates this claim is Psalm 132, verses 7-8 and 13-14, which describes the temple in Jerusalem as the 'resting place' and 'dwelling' of God. This temple concept is further corroborated when he look back to day 6, where we find humanity is created as 'the image of God', i.e. God's temple icon.

The necessary conclusion then becomes that the universe that has been created on days 1-6 is God's temple. When God 'rests' in the universe he has just created, it means his presence has come to dwell in his cosmic temple.

In the Gospel of John it is written in 4:24 that God is a Spirit and spirit don't need rest or sleep. He is alive mighty God and if God sleeps then He is not a God. According to Psalm 121 our God neither sleeps nor slumbers.

The confusion about God resting comes from the translation of the original word used in Hebrew.

That original word was:

שָׁבַת

shabath (shaw-bath') v.

1. to repose, i.e. desist from exertion

2. used in many implied relations (causative, figurative or specific)

KJV: (cause to, let, make to) cease, celebrate, cause (make) to fail, keep (sabbath), suffer to be lacking, leave, put away (down), (make to) rest, rid, still, take away.

For some reason many people want to take the word to mean strictly to repose, or sleep, while disregarding it's most common usage which is to stop from exertion.

All Scriptures quoted are from the King James translation.

Genesis 2:1 through 3

1 Thus the heavens and the earth were finished, and all the host of them.

2 And on the seventh day God ended his work which he had made; and he rested on the seventh day from all his work which he had made.

3 And God blessed the seventh day, and sanctified it: because that in it he had rested from all his work which God created and made.

These verses make more sense when we substitute the word celebrate instead of rested and rested from especially in view of later references to the sabbath

Exodus 20:8 through 11

8 Remember the sabbath day, to keep it holy.

9 Six days shalt thou labour, and do all thy work:

10 But the seventh day is the sabbath of the LORD thy God: in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates:

11 For in six days the LORD made heaven and earth, the sea, and all that in them is, and rested the seventh day: wherefore the LORD blessed the sabbath day, and hallowed it.

Sometimes when I am doing something, especially if it is strenuous; I will stop for awhile and catch my breath, (I'm no spring chicken any longer) that may be called rest. However, when I have finished what I was doing I desist from working on it and that rest is different from the break I take in the middle of the task.

On those rare occasions when I do a really good job I have a tendency to step back and admire my work as I: so to speak; rest. That is much different from both of the rests described above.

Having considered all those things it seems to me that after:

Genesis 1:31 And God saw every thing that he had made, and, behold, it was very good. And the evening and the morning were the sixth day.

That might just have been what God did. And it also may have been the reason he commanded us:

Exodus 20:8 Remember the sabbath day, to keep it holy.

Perhaps he just might have wanted us to remember on that day once a week that it had only taken him six days to create all of this and give him thanks for doing it.

"Rested" = "Ceased"

The Hebrew word translated "rested" in Genesis 2:2 is shabath (7673, שָׁבַת) literally means: to cease, desist, rest. This is the origin of the word "Sabbath," the day of rest or the day on which no work was to be done.

I posit that "rest" here means something like "at rest" (i.e. an object that is not moving) as opposed to relaxing or sleeping. He "rested" because he had (v2) "completed His work which He had done" and there was nothing left to do. He "ceased" from working because his work was finished.

It isn't sensible to think that God sleeps (as pointed out by @Mawia), nor does the text in Genesis 2:2 support such an idea.