TLDR; Jesus is fully God, but decided to become fully human in order to save His people from sin, and to be an example for us. This limited Him, but did not cease to make Him God.
I believe the Bible answers this clearly.
In the beginning was the Word, and the Word was with God, and the Word
was God. 2 He was in the beginning with God. 3 All things were made
through Him, and without Him nothing was made that was made. 4 In Him
was life, and the life was the light of men.
Jesus is completely God.
"In the beginning was the Word."
Jesus "was" when time began. Jesus is outside of time. He is God. He is also the co-Creator,
"All things were made through Him, and without Him nothing was made
that was made."
He is part of the Elohim, He was there when God said,
Let Us make man in Our image, according to Our likeness...
Then Jesus took on the form of humanity to save us from our sin.
And the Word became flesh and dwelt among us, and we beheld His glory,
the glory as of the only begotten of the Father, full of grace and
He was equal with God, but He chose to take on a human form for you and me.
Let this mind be in you which was also in Christ Jesus, 6 who, being
in the form of God, did not consider it robbery to be equal with God,
7 but made Himself of no reputation, taking the form of a bondservant,
and coming in the likeness of men. 8 And being found in appearance as
a man, He humbled Himself and became obedient to the point of death,
even the death of the cross. 9 Therefore God also has highly exalted
Him and given Him the name which is above every name, 10 that at the
name of Jesus every knee should bow, of those in heaven, and of those
on earth, and of those under the earth, 11 and that every tongue
should confess that Jesus Christ is Lord, to the glory of God the
A child was to be born who would be called "Everlasting Father".
For unto us a Child is born, Unto us a Son is given; And the
government will be upon His shoulder. And His name will be called
Wonderful, Counselor, Mighty God, Everlasting Father, Prince of Peace.
His name was Jesus, the name means Yahweh is Salvation or Yahweh the Savior. The Angel clearly points to Jesus as Yahweh, or God, the Savior for He shall save His people from their sins.
But while he thought about these things, behold, an angel of the Lord
appeared to him in a dream, saying, “Joseph, son of David, do not be
afraid to take to you Mary your wife, for that which is conceived in
her is of the Holy Spirit. 21 And she will bring forth a Son,
and you shall call His name Jesus, for He will save His people
from their sins.”
When He took on human form, He used the same power available to us. He prayed,
Now in the morning, having risen a long while before daylight, He went
out and departed to a solitary place; and there He prayed.
He learned the Word from when He was a child,
Now so it was that after three days they found Him in the temple,
sitting in the midst of the teachers, both listening to them and
asking them questions. And all who heard Him were astonished at His
understanding and answers.
and through His relationship with the Father, He did many miracles. Not of His own power, but with the power of the Father.
6 Jesus said to him, “I am the way, the truth, and the life. No one
comes to the Father except through Me.
7 “If you had known Me, you would have known My Father also; and from
now on you know Him and have seen Him.”
8 Philip said to Him, “Lord, show us the Father, and it is sufficient
9 Jesus said to him, “Have I been with you so long, and yet you have
not known Me, Philip? He who has seen Me has seen the Father; so how
can you say, ‘Show us the Father’? 10 Do you not believe that I am in
the Father, and the Father in Me? The words that I speak to you I do
not speak on My own authority; but the Father who dwells in Me does
the works. 11 Believe Me that I am in the Father and the Father in Me,
or else believe Me for the sake of the works themselves.
He was fully man and fully God, though His divinity was mostly hidden by humanity for our sake. To show us how to live and show us that all that He did is within our reach.
For I have given you an example, that you should do as I have done to
you. 16 Most assuredly, I say to you, a servant is not greater than
his master; nor is he who is sent greater than he who sent him. 17 If
you know these things, blessed are you if you do them.
... and even greater things than He did.
“Most assuredly, I say to you, he who believes in Me, the works that
I do he will do also; and greater works than these he will do, because
I go to My Father. 13 And whatever you ask in My name, that I will do,
that the Father may be glorified in the Son. 14 If you ask[c] anything
in My name, I will do it.
Nevertheless, because He was human, not everything was revealed to Him, as you point out. This however, does not mean He is not fully God, as pointed out previously.