The only logical explanation is that San Andreas replaces both California and parts of Nevada. I know a lot of people assume the map is a set of islands therefore it has to be interpreted as such, but really it makes no sense realistically and since this is a roleplay server then we should make sure what we consider SA to be is accurate to reality. The State of San Andreas has its own lore and history; it is based on that of California's, with slight variations especially as to insert innuendos here and there. In the universe the game takes place in, we have our own brands (Cluckin' Bell, ZIP, etc.), we have different landmarks and a different history (in this universe, California and Nevada are one state, SA).
Yes, San Andreas is a fictional state, but that does not mean it is a 51st state. It doesn't exist in real-life (hence why it is fictional), but in this world San Andreas is a state, and replaces the region it takes inspiration from.
Rockstar Games design their maps as islands so no part of the map is inaccessible to the player, they've always done this, in GTA 5 they explicitly call the body of water north of Paleto Bay a river even though it's designed as an ocean. I don't believe for one second that a map that shares so many similarities with real-life California and Nevada co-exist alongisde each other. The northern parts of the map are rock formations whereas the south and west parts have natural beaches.
The map is not an accurate representation of the state, it's geographically inconsistent, small, the highway system is redundant, and quite literally impossible due to its shape. It was designed in such a way that all the space that is taken isn't wasted, when you look at it. It just serves as the platform to roleplay on. In reality, you have to pretend as though the map is bigger (there are businesses that are mentioned in the game but are nowhere to be found in the map, such as a high school in Palomino or the theme park). Also consider that the map would be 60 times bigger compared to single-player, because 24 hours in SP is 24 minutes.
There are too many things that hint to San Andreas replacing both California and Nevada.
The State itself is named after San Andreas, the fault line that goes through California. If you know where the line goes through in real-life, it isn't located in the ocean. Yet in San Fierro Bay you can clearly see the fault line underwater, because IRL the line goes through San Francisco the same way.
The signs in Red County indicate that towns like Palomino Creek etc have populations in the thousands, even though they're ridiculously small cities. In-game Los Santos has a population of three million, yet the map is 33 miles square, it would mean the density/pop would have to be three times higher than Mumbai.
And also when you look at all the locations in the game, 95% of them are straight up copies of real-life locations.
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Los Santos -> Los Angeles
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San Fierro -> San Francisco
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Las Venturas -> Las Vegas
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Idlewood -> Inglewood
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Pershing Square -> Pershing Square
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Vinewood -> Hollywood
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Vinewood Walk of Fame, Vinewood Boulevard -> Hollywood Walk of Fame, Hollywood Boulevard
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Red County -> Orange County (& Kern County)
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(Windy Windy Windy) Windy Street -> Lombard Street
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La Conca -> La Concha Motel
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The Strip -> Las Vegas Strip
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Gant Bridge -> Golden Gate Bridge
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Mount Chiliad -> Mount Diablo (& Mount Whitney)
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Sherman Damn -> Hoover Dam, Nevada
I could go on and on.
It makes the most logical sense. I also roleplay hours passing when travelling from one city to the other, and despite not physically being possible, roleplaying driving out of state in-character on several characters before.
As a general rule I roleplay everything as if it were the real-life universe unless there is a 3D Universe equivalent. So Liberty City replaces New York, Vice City replaces Miami, Carcer City replaces Philadelphia, Pfister replaces Porsche and Ferrari replaces Grotti, I mostly stick with in-game brands because we're in a video-game, not real-life. You don't have KFCs, instead they're Cluckin' Bells.
This is what I've always roleplayed the United States to be while RPing on SA-MP.

I made a thread about this back on the LS-RP forums where I go more in-depth with this. Here's the link: https://forum.ls-rp.com/viewtopic.php?p=7483263
Perhaps while the server is in development the opportunity should be taken to decide what SA is, as opposed to leaving it ambiguous because it would "mess with people's backstories."
As for why the rest of the map would be closed down (Los Santos and Las Venturas), I would like to believe that there was an unprecedented natural disaster such as an earthquake which struck most of the State of San Andreas, leading to the cities being evacuated, coupled with a man-made catastrophe such as toxic waste being released and water being contaminated, ultimately resulting in the depopulation of LS and LV and a population migration to San Fierro and other states. If the server expands and extends to those affected cities, then the reason can easily be that those cities now are below toxic levels and can be repopulated.