I'm not sure I
want to envision what a movie series
beginning in 1948 (obviously if it were successful it would go on for years after that) version of Trek would
realistically be like, with realistic budget, realistic production values, realistic casting and politically easy-to-accept back story and implied values. Indeed there almost certainly couldn't be more than a small fraction of the boundary-pushing internationalism and lack of racism and gender integration that the Original Series managed OTL--often over the kicking and screaming of 1960s network executives. (Another battle royale Roddenberry had to fight, OTL, alongside casting women in any roles whatsoever, and casting an African-American one as an officer, was preventing the Enterprise crew from smoking cigarettes. Network executives were displeased at that too...

) Aside from such socio-political things, I shudder to think what the sets and props would look like on a B-movie budget.
So the OP cannot realistically hold; it's ASB.
On the other hand, as an ASB thread with the production designed for maximum awesomeness, with a deep-pockets producer determined to take the political flak and willing to shell out money for production on an A-movie scale for say 6 bimonthly episodes and blockbuster scale for an annual cliffhanger--man, that could be fun!
Agreed you can't get more than one big star (though the secondary characters might become stars!) You can't even get one big star since they are all contracted to some studio or other.
Scenario--someone from our times is ISOTed to the early 1930s. Fortunately for them they are an electrical engineer--let's say it's a man to smooth the path a bit. He demonstrates some significant advance in electronics, goes to work for RCA or someone like that, gets funding for advanced projects like solid state devices--invents an early, primitive transistor for instance. He's also politically and economically savvy, so he manages, despite contracts with corporate employers, to get a chunk of serious income and control of the inventions out of the process. Come WWII, he parleys his inventions and track record into contracts to develop some highly advanced stuff for the war effort under his own name, and emerges from the war as an electronics mini-mogul. The most advanced cutting edge tech the USA now has, somewhat shared with the British and stolen by the Russians, is now the better part of a decade more advanced than OTL. The state of the art of normal, consumer electronic tech is significantly ahead of OTL too, and is about to be transformed by this guy's wholesale marketing of solid-state systems--radios, then televisions, and other stuff. He's not the only one in this business but he's the leader. By 1948 he's making money hand over fist.
He's determined to do some good in the world (beyond helping the Allies win the war somewhat earlier as happened) with his wealth and influence. He happens to have been a Star Trek fan before being ISOTed. So at this point, he funds an independent studio of his own to realize the dream. He obviously has to take Roddenbery's place as
auteur of course! But I daresay in 1948 he could recruit a whole slew of top-notch actors, directors, craftsmen and technicians no one has ever heard of OTL (or did, but wouldn't until later).
As for the politics of casting an African-American woman as com officer (Dorothy Dandridge might indeed be available, and might be the most famous name he has on the marquee!

), having a young lieutenant from Leningrad, and so forth--1948 might actually be a better year for that than 1964. Or no worse. 1954 would be the worst time. The Cold War was a political phenomenon and getting the ball rolling took some time in the West. In 1948 a lot more leftist opinions had a larger accepting audience than just a few years later. The same goes for feminism--by 1948, the backlash against women in public positions Betty Friedan describes in
The Feminine Mystique was getting rolling but it had just begun. As for race relations--I will admit, by 1964 several factors had made assertions of racial equality as America's new norm or at any rate goal more defensible against the white supremacists. Several key Supreme Court decisions had by then undermined the legitimacy of Jim Crow and legal segregation--not however yet
Virginia v Loving, which struck down miscegenation laws--that wouldn't happen until Trek had gone off the air, or at any rate not until the middle of the third season! So the "interracial kiss" scene between Kirk and Uhura was actually still criminal at the time it aired in many markets!
What I'm suggesting is, a private backer with deep pockets and an uncompromising vision that Jim Crow had to end and Americans could and would embrace multinationalism and interracialism within a generation, and women's lib into the bargain--could get a story that pushes the boundaries in 1948 put onto film--and there would be audiences that would be glad he did. Alongside them, if he's clever at not slapping the public norms in the face at every turn but instead getting stuff in under the radar, will be others who didn't think of themselves as pinkos but come for the tech spectacle--and leave, some of them, wistfully wondering why today can't be more like that imaginary future.
I'm not saying that one sci-fi series can transform the American mentality en masse. I'm suggesting that the conformity of the 1950s actually was a facade that masked a much greater diversity of thought and opinion than was deemed respectable, and that one SF series might become a rallying point for progressively minded people to stand up and be counted.
If our ISOTed mogul does cast Dorothy Dandrige as Uhura, the films probably won't be shown in many states. If he ever has her kiss some white guy--they might actually become felonous, or at least some kind of misdemeanor incitement to crime, in perhaps a majority of states at this time.
But if the series can establish some popularity, enough to pay the bills, and gain some allies in some key audiences, he might be able to hold off, by being strategic which markets he releases the film to.
A big stumbling block, by the way, is that in the golden age of film movie theaters were not independent operations--they were associated with a particular studio, generally. It might be very difficult for him to find venues in which the movies can be shown in most of the country, quite aside from being controversial.
It is a tall order, but I like imagining what the "awesomeness over all" version of Trek might have been like in the 1950s. Since it requires a time traveller or other prescient, I'd sadly say this is the wrong forum for it.