Was man judged at the cross along with Satan and the rebellious Angels? In Matthew 5:22 Jesus says that anyone who calls another a fool will be in danger of Hell fire
Matthew 5:22  KJV

But I say unto you, That whosoever is angry with his brother without a cause shall be in danger
of the judgment: and whosoever shall say to his brother, Raca, shall be in danger of the council:
but whosoever shall say, Thou fool, shall be in danger of hell fire.

and in the Revelation Chapter 20:14 it tells us that Death and Hell will be thrown into the lake of fire:
Revelation 20:14  KJV

And death and hell were cast into the lake of fire. This is the second death.

Also in the story about Lazarus and the rich man:
Luk 16:22 through 24  KJV

22 And it came to pass, that the beggar died, and was carried by the angels into Abraham's bosom: the rich man also died, and was buried;
23  And in hell he lift up his eyes, being in torments, and seeth Abraham afar off, and Lazarus in his bosom.
24  And he cried and said, Father Abraham, have mercy on me, and send Lazarus, that he may dip the tip of his finger in water, and cool my tongue; for I am tormented in this flame.

Apparently some go to Hell when they die and are tortured by the heat (fire) and at the Great White Throne judgment are then thrown into the lake of fire.
Revelation 20:15  KJV

And whosoever was not found written in the book of life was cast into the lake of fire.

Revelation chapter says nothing about either Satan, His minions being judged only thrown into the lake of fire.
It does say that the dead are judged but only for their works:
Rev 20:12 and 13  KJV

12 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.
13  And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.

Does it seem possible that unbelief is judged along with Satan and his minions at the Cross, and the Great White Throne judgment is for what wrongs they have done on Earth?
Mankind was not judged at the cross.  Rather, judgement began - and per that, for the household of God, not mankind en masse.

As for Satan, he's been judged, Jn 16:11.  But, the sentence has yet to be carried out, Rev 20:2.  He will get a temporary brief from that incarceration, Rev 20:7.  Then, have a permanent sentence carried out, Rev 20:10.

Back to mankind, judgement has now begun with the household of God, 1 Pt 4:17.  The scripture's "household of God" can be loosely interpreted as "Christians" today.  However, keep in mind mainstream religion is not a spiritual body, rather an institution of man, e.g. Matt 13:24-30, I Cor 10:5-6, Rev 17 and more.  

The rest of mankind that is not "the household of God" has not entered into judgment, Rev 20:5.  They will enter into judgement later, Rev 20:12.

The reference you make to Luke 16:22-24 does not support the poor man died then went to heaven immediately.  To make that assertion, one would have to throw out the explicit references in scripture that is not the case, e.g. Heb 11:39-40, Jn 6:44, 54, I Cor 15:51-52.

(Many also use Lk 23:43 in the same context.  There is no punctuation in the original Greek.  We know the criminal on the cross is not in heaven per the scriptures above, among many, many more).

So, one one's dying and going to heaven, or hell, upon the first death.  That's explicitly not the case in scripture.  (And, popularity of a belief makes it no more true, scripture is the final authority). 

So, in conclusion: judgement began - for a part of mankind, the "household of God" with the cross.  The rest of mankind enters into judgement later.  Satan is on his own "judgement plan" with God.  (And, there's a fourth category, 1 Cor 6:3 concerning the judgement of angels).