Someone provided a good method in this Reddit post. It worked when I tested it. This was still the top result when I searched the question, so I'll paraphrase/add some details below for those who need it.
To get an unnamed Persian in Pokemon Sword or Shield without transferring* anything, you need to breed** a non-Galarian Meowth or Persian that is holding an everstone, then hatch and evolve the resulting non-Galarian Meowth.
The only two candidates for parenting your first non-Galarian Meowth that were available when the game first came out are the Meowth (or Persian, if you already evolved it) named Cash that you get from an in-game trade with a kid to the left of the runway in the lobby of the grass gym in Turffield, and the non-evolving, gigantamax-capable longcat meme Meowth that was obtainable via mystery gift when the game first came out. Both of these are male (for me at least), so they must be paired with a Ditto*** in order to produce a Meowth. They are also both vanilla/Kantonian variants, which means that as of now Alolan Meowth and Persian are unobtainable without hacks (though you can go see an Alolan Meowth in Marisa Luisa’s campsite on Route 7 if your game's version is up to date).
As the Reddit post mentions, the offspring of a parent Pokemon holding an everstone inherit not only that parent's regional variant, but also its nature; so, if you want a Persian with a specific nature, you will need to buy the corresponding nature mint from the lady at the far left side of the left counter on the first floor of the battle tower and use it on the unnamed Meowth/Persian (or the Meowth/Persian parent from which the unnamed one inherits***, prior to breeding it).
Side note: The Reddit post only mentions Persian and Cofagrigus, but this method is also necessary for duplicating Kantonian Mr Mime, since Mime Jr. always evolves into Galarian Mr. Mime in Pokemon Sword and Shield. The tainted, non-renamable Kantonian forms of Yamask (which evolves into Cofagrigus instead of Runerigus) and Mr Mime can be obtained from in-game trades with the poke kid in the Eevee costume on the left side of the fairy gym in Ballonlea and the team yell grunt in the booth just left of the dark "gym" in Spikemuth, respectively.
* Pokemon Home probably offers
another, easier way to get a
Persian via transfer, if you have it. I
don't, so I'm not sure. If it doesn't now,
it likely will eventually.
** Breeding is accomplished by leaving
two compatible Pokemon in the same
Pokemon Nursery together for about
20 minutes. Two Pokemon are
compatible if they are in the same
[egg group] and of opposite sexes,
or if one of them is a Ditto and the
other is at least capable of breeding.
Certain Pokemon, such as legendaries,
cannot breed at all.
There are two Pokemon Nurseries in
the game. One is on Route 5, and the
other is in Bridge Field in the wild
*** When two Pokemon that are not
both Ditto breed, their offspring's
species will always be the same as the
mother's. So if you want to replicate a
male Pokemon, you will need to breed
it with a Ditto.
Ditto spawn in all weather in the
grass at the Lake of Outrage (not as !s,
but as rare-ish overworld spawns), as
well as randomly appearing in max
raid battles in [den #66]. I'd grind
for a good [five-star max raid Ditto]
if you want your Persian to have the