The subject of the title stems from numerous discussions I've had with fellow DMs and players, in regards to a PC I've played twice. A house of Cannith, Mark of Making Human Artificer.

Long story short, he saw the creation of the Warforged, and believed that the discrimination problem would be solved if they had someone, "up top" to vouch for them...that and he wanted to see if he could do it. Along the way, he makes a number of things as he levels up, mostly on the scale of prosthetics, weapons, etc. (normal artificer stuff). Then he gets fun and makes a battle armor (think Ironman but steam punk), then starts designing a "bigger version of that, but capable of fighting giants and dragons". 

But I'm digressing.
The key point, that fell through before both games ended, was "How would you go about making a mechanical god?" and "How do you go about making a fantasy Mecha?". We had answers ranging from killing a God, lichdom, dragon blood, psionics and one dude even suggested going to Cult to grab the Soul harvester and make a hive mind XD.

Both of those games are over now, but it left me wondering how, in a D&D setting, you could make a warforged god. Any ideas?

Firstly, this sounds amazing.  I have a couple possible origin stories or variations.  

Option A:  I would picture some sort of dying god of invention or knowledge, who just so happens to have an iron giant, animatron type construct as it’s second hand.  As the god begins to become weaker and weaker the robotic assistant becomes taking over more and more for god.  Eventually through either an act of thanks or epiphany of righteousness.... or even a fever dream in its last moments.  The gods final act is to give consciousness to his mechanical assistant and hands the mantle over to him.  The First Warforged:  he looks upon the world and sees how “his people” are treated and begins giving them artificial intelligence as well.

Option 2:  Picking up where you left off with the Warforged Knight that continues to grow in size and power eventually takes on a challenge or power that results into a catastrophic explosion, resulting it leaving its corporeal body and becoming a stream of consciousness and power.

Option III:  begin with same idea as option 2, but instead he rockets into space eventually colliding with an elder power causing an amalgamation of godly power, mechanical engineering, and knowledge of the ancients.

Option Delta:  your Warforged gets bigger and more powerful and quests to find specific pieces of metal to make a special armor out meteorites or something.  Making his new armor, he then passes through the divine gate as he exploits a loophole due to him not being a “living person”

What about the Kuo-Toa?  

Perhaps they worship the PC and cause this god you want to be manifested?

Maybe your PC finds out about the Kuo-Toa, the lore surrounding their god and works to get them to worship the warforged?

Or you don't, a (war)forged god makes itself.

Isn't Moradin the god of the forge?

In Pathfinder, there are Ascendant AIs called "Iron Gods" who achieved divinity through a combination of magic and technology. It could be reskinned and mage-splained away with something like an eldritch machine capable of granting godhood to a mortal construct. There's also the Raven Queen, who Ascended to godhood through a means now lost but perhaps rediscoverable. In Brandon Sanderson's books, one can achieve apotheosis by killing an existing god and taking his or her power.

You could also appropriate the goddess Brigh from the Pathfinder pantheon, who counts sentient constructs among her faithful.

Consider the lord of Mechanus, Primus.  Or something similar to this being, he created the modrons (or perhaps splintered them off from himself) but I could see this being having created more humanoid versinos to gain more knowledge of things like emotions or just the 'human' condition (general term not specifically the human race).  Send out seeds of warforged to someday bring back the knowledge being mortal.  Gotta log every piece of knowledge in the universe.