I asked a question beforehand asking whether if there was a way for an artificer to make an item that can cast epic spells and after learning the answer was no i decided to look for other ways an artificer to create epic spells.
Infusions themselves cannot qualify
In addition to skill ranks that are no problem for any epic-level character, Epic Spellcasting requires the ability to cast 9th-level arcane spells or 9th-level divine spells.
To begin with, per Eberron Campaign Setting page 31, infusions are spells, so that much isn’t a problem:
[Infusions] function just like spells and follow all the rules for spells
And, surprisingly enough, the artificer can get 9th-level infusions. As Player’s Guide to Eberron notes, an epic artificer can qualify for and take the Improved Spell Capacity epic feat, using the higher-level infusion slots for metamagic’d infusions. This is consistent with Eberron Campaign Setting, which notes (again on page 31) that
Like a spellcaster, an artificer can apply [...] metamagic feats to his infusions. Like a sorcerer, an artificer can apply a metamagic feat to an infusion spontaneously, but doing this requires extra time.
So the artificer can get 9th-level infusions. He may have to use Heighten Spell for them to count, but he can get them. However, Eberron Campaign Setting page 31 also notes:
Infusions are neither arcane nor divine;
and that means infusions will never qualify for Epic Spellcasting, no matter what level the artificer gets them to.
Magic items almost-certainly won’t allow anyone to qualify
Alternatively, you could make a torturous argument that when you activate a spell-completion item, you cast that spell, so if you had a staff with 9th-level spells, you would be casting 9th-level spells. And since you can do it, you are able to do it, so you have an ability to do it. None of this holds up to even the most casual comparison to the overall wording used by the rules text—meeting a requirement for an ability to cast spells consistently means having your own spell slots from your own class levels.
Also, even if this worked, someone else would have to make the item for him. Like infusions, the spells cast by spell-completion and spell-trigger items created by artificers are explicitly neither arcane nor divine, according to the errata for Eberron Campaign Setting, so they don’t help you any more than infusions themselves would.
I suppose you could also try to claim a magic item that uses shapechange or something to become a creature with innate high-level spellcasting could arguably work. Again, this becomes an ugly mess of tortured language that only works if you really, really want it to.
And note that, as a feat, Epic Spellcasting requires you to meet its requirements any time you want to use it. You cannot use anything that temporarily gives you spell slots, take the feat, and expect it to work later.
This is a good thing, because Epic Spellcasting—Epic Level Handbook wholesale—is broken
The epic level rules do not work. They do not provide a stable, playable game system that continues past 20th level, as they claim to do. And Epic Spellcasting is by-far the worst offender in the book.
Meanwhile, the artificer was designed for Eberron Campaign Setting, a world in which mortals top out around 10th level—not even 20th. The entire game world was scaled down, in part, precisely to avoid the problems with high-level and epic-level play. In its own setting, no artificer has ever attained 20th level: see Player’s Guide to Eberron page 17:
First, it’s probably best to assume that player characters who reach epic levels are among the first people to accomplish such a feat, at least in recent memory. [...] In the current age, it is possible that no one has exceeded 20th level, which means no member of the common humanoid races has ever done so before.
It also means no artificer has ever done so, because artificers only started to be a thing after the discovery of the Mark of Making and the creation of House Cannith. That is well into the current age. (Player’s Guide to Eberron, of course, leaves the door open just enough for DMs to decide that in their Eberron game, there are epic-level mortals—but the authors did not recommend it and certainly appear to not consider such a thing part of their conception of Eberron.)
Anyway, the highest-level artificer mentioned in the books is Merrix d’Cannith (9th-level artificer/3rd-level dragonmark heir, per Eberron Campaign Setting page 232). Eberron would be a very, very different world if there were an artificer better than Merrix d’Cannith, since he, following in his father’s and grandfather’s footsteps, is almost single-handedly responsible for the technological state of Khorvaire as we find it (with a nod towards Zilargo for mastering elemental binding). The only way to justify a higher-level artificer existing without upsetting the world as presented would be for that artificer to basically have shut themselves away and not interacted with the rest of the world at all—which is a trope that Eberron generally goes out of its way to avoid.
So please, do yourself a favor, and if you’re playing in Eberron, do the game-world a favor, and reconsider attempting to use the epic rules. If you insist, please at least ban Epic Spellcasting. And if you insist on having it, you are then absolutely required to have it. You cannot participate meaningfully among people who have it if you do not yourself. Epic Spellcasting has become the entire game, because it will always have the best answer to every problem and the only question is how to abuse mitigation to get Epic Spellcasting to do what you want. Whatever it is, will absolutely guaranteed be the most effective and efficient thing you can do to solve whatever problem you have, so there is no reason to consider other approaches or interface with the rest of the game’s rules at all.