Ask Your DM (Nicely)
The DM is allowed to change some (read: all) of the rules as they see fit. On page 287, there is a subsection titled Changing Spell Lists. By simply asking your DM, they may decide that Rule of Cool wins here, and let you select it. You may wish to suggest removing some other spell from their list, but honestly for Sorcerers, this is pretty lame. You'd have had to ignore some of those level 7 spells anyway unlike, say, Clerics.
Make Friends With A Wizard, Then Ask Your DM (Nicely)
Wizards are all about arcane research. Ask your DM what it would take for such a researcher to invent a new spell, ritual simulacrum, which behaves exactly as simulacrum but has the ritual tag (see DMG 283, Creating a Spell). From there, your sorcerer would need an int or wis of 13 or higher for the Ritual Caster feat. From there, simply copy it into his ritual book.
Beg a Blessing From Your DM (Nicely, of course)
Blessings (DMG 227) are supernatural gifts bestowed on a character. Generally, "a typical blessing mimics the properties of a wondrous item". I'm not aware of one that adds spells known like this specifically, but your DM may be willing to consider this an appropriate reward for some task.
These two feats should be fine, if a bit underpowered
In fact, I think you'll find that barely anybody will even take them. Wall of Water, for example, is a spell Tritons get once per rest, but you don't see people flocking to Triton because of that spell. Why? Because it really isn't that big a deal, I play a Triton Fighter and I've used it like 3 times total.
You have to remember that a feat means you're sacrificing an ability score increase (very important) or a different feat (can be important, depending on your build).
For a caster who can already cast third level spells, you're more likely interested in getting an extra +2 to your primary casting ability, rather than being able to cast Wall of Sand or Wall of Water once per rest.
They sound like great, fluffy additions to your campaign, and I expect players will absolutely completely ignore them because they're on the weaker end of choices you can make at a levelup.
Best Answer
17th level as a sorcerer or wizard; 17th level as a Genie warlock; 18th level as a bard; 17th level as an Arcana cleric
Wish is a 9th-level spell. It's only on the wizard and sorcerer class spell lists (and the Genie-patron warlock's spell list, as I mention a bit later).
Full caster classes (including sorcerers and wizards) gain 9th-level spell slots at level 17 in the class. Multiclassed spellcasters know/prepare spells as if single-classed, so you need at least 17 levels in either sorcerer or wizard to have a 9th-level spell slot and thus be able to learn the spell.
The Genie-patron warlock's Expanded Spell List feature also adds wish to their (9th-level) spell list. Unlike other full casters, warlocks can't learn 6th-level or higher spells (and their spell slots don't go above 5th level), but they do gain the Mystic Arcanum feature:
At 17th level, a Genie-patron warlock can choose wish as their 9th-level Mystic Arcanum spell, allowing them to cast wish once per long rest.
In addition, the wish spell isn't on the bard class spell list, but they can still learn the spell using their Magical Secrets feature:
Using the Magical Secrets feature, you can learn 2 spells from any class spell list at 18th level. As full casters, bards also get a 9th-level slot by that point, so they can learn wish using the feature.
Finally, Arcana Domain clerics get the Arcane Mastery feature at 17th level (SCAG, p. 126):
They could choose wish as their 9th-level spell from the feature. (Thanks to David Coffron for pointing this out!)
For magic items that can cast wish, it's up to the DM (but probably not much earlier than 17th level)
There are a few magic items that can let you cast the wish spell or cast it for you. However, it's up to the DM whether to even roll on the tables to determine treasure, or whether to allow you to gain items that let you cast the wish spell. Given how powerful wish can be, the DM might be hesitant to do so any sooner than you could normally learn the spell.
The lowest-rarity item, the efreeti bottle, is still listed as "very rare", and only has a 10% chance of giving you wishes:
On a roll of 91-00 on the percentile dice ("d100"), it gives the following result:
All but one of the remaining items that allow you to cast wish are legendary items. The first and probably most controversial is the deck of many things. Only one of the cards in the Deck, the Moon, lets you cast wish (with the other possible effects ranging from campaign-destroyingly good to campaign-destroyingly bad):
A much simpler item that lets you cast wish is the luck blade:
The ring of three wishes is probably the most straightforwardly named of the bunch, and does what it says on the tin:
And finally, the last item (or pair of items) is an artifact, the Eye and Hand of Vecna (DMG, p. 224). Attuning to both items involves some self-mutilation (and removing either one afterwards kills you), but you gain a variety of benefits and incur a few dangers. If you attune to both, the last benefit listed is:
There is, of course, the possibility (however unlikely) of acquiring a 9th-level spell scroll with the wish spell on it. Spell scrolls can only be used by those with the spell on their class spell list, so only sorcerers, wizards, or Genie-patron warlocks can do it (or bards who pick the spell with the Magical Secrets feature, but they'd already know the spell that way so it's kind of pointless for them). Note that even lower-level sorcerers/wizards/Genie warlocks could use a wish spell scroll, but they'd have to pass a DC 19 check using their spellcasting ability (Charisma for sorcerers and Genie warlocks, Intelligence for wizards):
The Magic Item Rarity table on DMG p. 135 suggests that very rare items be limited to 11th-level or higher characters, and that legendary items be limited to 17th-level or higher characters.
However, the magic item tables on the following pages do list specific magic items as possible treasures, and the treasure hoard tables do give guidance on randomly determining the contents of a large cache of treasure, whether that's the accumulated wealth of a large group of creatures, the belongings of a single powerful creature that hoards wealth, or a reward from a wealthy/powerful benefactor for completing a quest (DMG p. 133):
The efreeti bottle corresponds to a roll of 71 on the d100 on Magic Item Table H (DMG p. 148). Magic Item Table I (DMG p. 149) includes the luck blade (corresponding to a roll of 11–15), the deck of many things (81), and the ring of three wishes (94).
The table for treasure hoards corresponding to CR 5–10 creatures (DMG, p. 137) has two rows that involve rolling once on Magic Item Table H; following these guidelines, it's only possible if the DM rolls 99 or 100 on the d100 when determining the treasure hoard. In order to then get an efreeti bottle, the DM would need to roll a 71 on another d100 for the magic item table. (And in order to then have the efreeti grant you 3 wishes, they'd need to roll a 91-00 on the d100 when the bottle was actually used by a character.)
Alternately, the treasure hoard table for CR 11–16 creatures (DMG, p. 138) includes a few more rolls that could theoretically result in an item that lets you cast wish. If the DM rolls 83–92 on the d100 for the treasure hoard table, they can roll 1d4 times on Magic Item Table H (to potentially get an efreeti bottle). If they instead roll 93–00 on the d100 for the treasure hoard table, they can roll once on Magic Item Table I. (And they'd then need to roll an 11–15, 81, or 94 on the d100 for the magic item table to result in an item that can let you cast wish.)
Finally, the treasure hoard table for CR 17+ (DMG, p. 139) states that a roll of 73–80 corresponds to 1d4 rolls on Magic Item Table H; a roll of 81–00 corresponds to 1d4 rolls on Magic Item Table I.
Artifacts (such as the Eye and Hand of Vecna) are a totally different beast, beyond even the highest treasure hoard or magic item tables (DMG, p. 219):
All in all, the DMG does not really expect low-level characters to be able to cast wish even through magic items. You can only expect to have a fairly significant chance to get a magic item that lets you do so once you're already high enough level to cast the spell (assuming you don't multiclass). This is probably at least somewhat by design, given that even the spell description begins:
Frankly, you're better off talking to your DM about finding a way to cast simulacrum directly rather than trying to cast wish to replicate its effect, given how potentially world-changing (and campaign-affecting) wish can be.