Firstly, that particular verse is taken out of context. It does not refer to the time on Earth (as in, the day/hour format of time we know of). The quotation from Mark 13:32 is from a larger section of text where Jesus discusses the exact time and date that the end of days will begin.
Mark 13:32 specifically states that Jesus, as the Son in the Holy Trinity does not know this exact date/time that God will begin the end of days (i.E. What Revelations describes). He states that only the Father knows this date ahead of time.
Jesus is omniscient, as far as we are able to tell, in all other matters. There are many other times in the Bible that shows that Jesus had knowledge of events in the future or of other human beings' thoughts that no regular person would have (such as in Matthew 16 when he predicts his death, or in John 4 when he knows specific details about the Samaritan woman's life).
Now, it is unknown whether this omniscience comes from God the Father or from the simple fact that he was the Son of the Trinity, but the fact that he was omniscient is undeniable.
Jesus, being both fully man and fully God, has a dual nature. His human nature is susceptible to human experiences like pain, hunger, and lack of knowledge. However, His godly nature, or the part of Him that is the Son, is omniscient, omnipotent, and omnipresent just as the God the Father is. It's complicated.
Before the Incarnation :
1. Just call the Logos as a "SHE".
2. She is God in heaven.
3. She is God with one nature, Infinite.
4. Just call her nature is God nature.
Human has one nature.
Call this nature is Human nature, Finite.
In the Incarnation condition :
1. She is a male human baby on earth.
2. This human baby we call as a "He".
3. He is finite.
SHE is the one who has two natures because SHE is preexisted before "He" exist on earth.
As God with her God Nature, It's impossible SHE cease to exist in heaven just because she appear at one particular place in a human male baby form.
At the time the male baby is in Bethlehem, SHE knows that part of her is in Bethlehem as a male baby. SHE knows everything that happens, What will happen and what has happened on earth.
But her human nature in a male baby form (as He) doesn't know everything that happens, What will happen and what has happened on earth.
Move him (the baby) from the bedroom to the kitchen, Then in the bedroom he is not there anymore.
SHE can move Him to other place faraway, But He cannot move himself to other place faraway YET let alone He moves Her.
Before the incarnation SHE knows the consequences to appear in human form with human nature, That is FINITE. So, Right after the incarnation, It is SHE who at the same time has two natures - both infinite and finite.
It cannot be He who at the same time has both infinite and finite natures because He is the second nature of her (finite) which exist later on.
God anointed Jesus of Nazareth with the Holy Spirit and power, And how he went around doing good and healing all who were under the power of the devil, Because God was with him.
The fact the He did miracles is because SHE anointed Him with the Holy Spirit and Power, Because SHE is with Him, Her second nature in a human male form. In Her divine nature, As God, SHE doesn't need anything and SHE doesn't grow in wisdom and stature. But her second nature, The human male, He need something and He does grow in wisdom and stature.
So, No. . . He is not omniscient.
The fact that He knows the future or the things which impossible that human can know, It is because SHE told Him about it in time not because He knows everything since a baby.