How could Cain have built Enoch?

Because the ground would never prove bountiful for Cain after his murder of Abel (Genesis 4:11-12), Cain likely taught some of his family to work the fields so that they could still reap its benefits, while he did something else that would benefit them. This provides the idea of a city with people having various occupations.

Perhaps at this point, he began hunting to find food. This would require a bit of traveling. His descendants (6 generations) raised cattle and became experts with iron and brass as well as instruments (Genesis 4:20-22). Where were all of these animals and metals found? Considering the long life spans they had, it is possible that Cain noticed these metals on his many journeys and had part in beginning some of these crafts, as he certainly wouldn't be profitable in farming anymore.

I have often thought that Cain fulfilled the Lord's curse against the serpent, and was perhaps the incarnation of the Serpent as an earthling, through some kind of trickery. Cain was driven out from the face (surface) of the earth, even hiding from the face of the Lord. The earth would not yield (The ground would be hard, he couldn't make anything rise above it). This suggests that he went below the surface as well as hiding in shadows (even histed to 'shadow' or 'providing shade'. This could indicate that he tunneled below, and that Enoch was an underground city, thus fulfilling the curse against the serpent who would "crawl on his belly" and "eat dust". In some places the serpent was referred to as the worm. Jesus reaffirms its idea by mentioning "the father below" who is the father of lies and the first murderer (Cain).

Nothing there says he was an "eternal" wanderer. It says he will be a "fugitive" and a "vagabond" - in other words, a criminal.

If you go on further you see that Cain was marked by God so no one would kill him (the appropriate punishment for murder, as seen later in the Law given to Israel through Moses). He subsequently left the "Presence" of God, and fled to the land of Nod to live there. No where does it say he would wander, and certainly not eternally.

Genesis 4:12->16, KJV.

12 When thou tillest the ground, it shall not henceforth yield unto thee her strength; a fugitive and a vagabond shalt thou be in the earth.
13 And Cain said unto the LORD, My punishment is greater than I can bear.
14 Behold, thou hast driven me out this day from the face of the earth; and from thy face shall I be hid; and I shall be a fugitive and a vagabond in the earth; and it shall come to pass, that every one that findeth me shall slay me.
15 And the LORD said unto him, Therefore whosoever slayeth Cain, vengeance shall be taken on him sevenfold. And the LORD set a mark upon Cain, lest any finding him should kill him.
16 ¶And Cain went out from the presence of the LORD, and dwelt in the land of Nod, on the east of Eden.

Here's the problem. The translation you're using is not a very good translation. This is the verse you're referring to (in a translation that actually supports your argument):

In Genesis 4:12 (NIV), God tells Cain

When you work the ground, it will no longer yield its crops for you. You will be a restless wanderer on the earth.

The phrase here, "then in moaning and trembling you will be upon the earth". That is what is often translated as "restless wanderer" or "fugitive and vagabond"

Why? Well, let's dig in:

stenochōria Strongs 2532 dire calamity, extreme affliction

kaiv Strongs 2532 and etc

tremō Strongs 5141 tremble, to fear, be afraid

eimi Strongs 1510 to be, to exist, to happen, to be present

epi Strongs 1909 upon, on, at etc

ho Strong 3588 this, that, these

gē Strongs 1093 arable land, ground, the earth as a whole, a country, region, etc

So, the idea is with "[dire calamity/extreme affliction] and [trembling/fear] you [will exist/be present] upon [the earth/the land/the region]".

That doesn't really say anywhere that he will wander or that he will never stop wandering. However, if you combine these two concepts: fear and affliction, it's understandable that the translators could interpret that as someone who would wander.

If I was full of fear and troubled with distress, I would probably wander as well.

However, having said this, I have no idea why they chose that translation. It seems to be a poor translation of this phrase.

Given a decent understanding of the curse, it should be easier to see that building a city and being fearful and in distress do not conflict.