Let's use Fighter McFighterson as our test case.
As a level 1 variant human, McFighterson takes the Magic Initiate feat. Mage Armor is his choice, let's say (alongside two, inconsequential, cantrips).
Does this allow McFighterson to create a potion/scroll/etc of Mage Armor? (assuming that the item is craftable by a "proper" spellcaster)
Page 128 of the DMG describes the requirements for crafting magic items, and specifically states
The character must also be a spellcaster with spell slots...
Although the Magic Initiate feat (arguably) does turn a non-spellcasting character into a spellcaster, it does not give a character spell slots; it only gives a character cantrips and the ability to cast a single non-cantrip spell once per long rest.
The alternate, and wholly optional, system for crafting magic items presented in XGtE, at p. 128, permits any character to craft a magic item, not just spellcasters. (Whether they have the Magic Initiate feat remains irrelevant.) However, the character does need some applicable proficiency:
To complete a magic item, a character also needs whatever tool proficiency is appropriate, as for crafting a nonmagical object, or proficiency in the Arcana skill.
There are two notable exceptions. First, brewing a potion of healing specifically requires proficiency with herbalism kit. Second, for spell scrolls, the crafter must indeed be a spellcaster. See XGtE p. 133.
The rules for crafting magic items can be found in the DMG.
From the DMG, pg 128-129, on Crafting a Magic Item:
To start, a character must have a formula that describes the construction of the item. Their character must also be a spellcaster with spell slots and must be able to cast any spells that the item can produce.
Since the Magic Initiate feat doesn't provide you with spell slots, only a spell, it does not qualify for crafting magic items.
Thematically, crafting requires the crafter to have an intimate understanding of the magic they are applying. So only someone who knows the spell well enough to be able to cast it can craft with it, and of course the only people who know spells well enough to cast them are (surprise!) the people who are capable of casting them. This is represented in-game by spells slots.
So someone who has a magic item or natural ability to produce the effect of a spell without a spell slot, does not necessarily understand the spell well enough to craft with it. Being a Planetar or owning a ring of spell storing with Blade Barrier in it will both let you cast Blade Barrier, but in neither case do you really understand the spell.
However, as @screamline notes, this understanding can instead be covered by a relevant skill, which again implies a certain level of knowledge in the crafter. I don't think it would be unreasonable for a DM to rule that magic initiate implies enough knowledge of the spell to craft with it, but it's not quite RAW on it's own. The question is, does Magic Initiate mean you have developer a (super)natural casting ability (like a Planetar), or does it mean you have intensively studied just that one spell until you have the knowledge to cast (and craft) it?
End of the day, if you want to allow the fighter to craft, you need to either give them something else (i.e. a multiclass, or a feat that grants slots, or the arcane proficiency with XGtE variant, etc), or use DM prerogative to tweak the rules a little bit.
