Let me elaborate. In things such as Game of Thrones and Lord of the Rings (so, high fantasy), fictional continents are quite often the setting. I don't recall ever seeing this in Science Fiction. My world does include both modern technology (cars, computers) as well as futuristic technology such as advanced aircrafts and exo-suits. The reason for wanting to set it on my own fictional continent is so I can create a unique world including a huge technologically advanced city to the North (technology is scarce in the rest of this world), deadly forests, and creatures that live in the wilds all on one land mass. I considered setting the story in a post-apocalyptic version of an existing country, but I don't think the world I envisioned would be quite as dynamic if I had to build it within a 'template'.
There's nothing wrong with doing so, and I can think of several examples where a sci-fi setting has been humans on a fictional world (or worlds). Typically but not always it's either explicit or implied that humanity has come to the world at some point from Earth but it's not essential. Often even where the Earthly origin of humanity is expressly stated it's little more than a footnote.
Bottom line is that if the story you want to tell is better told on not-Earth then set it there.
The examples cited by you of Game of Thrones and Lord of the Rings are both set in what are usually called Secondary Worlds. These are worlds essentially similar to our own, but with different yet still similar histories and geographies. So they can have lands and continents that do not exist in our own world. In secondary worlds inventing your own continents is simply par for the course.
Historically we have imaginary lands such as Atlantis, Lemuria and Hyborea. These fantasy lands were created at times when peoples understanding of geography and geological history was impoverished compared to the present era.
Fiction set in worlds which are ostensibly versions of ours can contain smaller imaginary bodies of land such as Treasure Island and Skull Island (as in King Kong). There is also the Soviet Union era novel set on the imaginary island of Crimea. Alas, I don't remember the author's name or the title of the novel.
Closest equivalent to what you ask is the British literary novel Continent by Jim Crace. This is set on a purely fictional continent. So what you want to do is not without precedent.
In principle there is nothing to stop an author from writing about a fictional continent. It's about time we had the new genre of alternative geography top match the well-established one of alternative history. Have fun with writing it.
Take a moment to consider the most famous Sci-Fi series that you can think of.
Is "Star Wars" one of them? How about "Firefly"? "Dragonriders of Pern"? Even - to a lesser extent - "Star Trek".
Sci-Fi not only regularly has fictional continents, but also fictional planets and galaxies, all with associated geography/cartography and political landscapes. Often these have semi-human inhabitants (to make it easier for the viewer or reader to comprehend), some of which have sometimes originated on Earth, but others haven't.
If you do not recall seeing fictional continents in Sci Fi, you should read more. They have been used extensively for several centuries, or even millennia. Perhaps, being more flexible with the definition of what Sci Fi is, might help you. No, I would never advise an aspiring author against using any tool they deem viable! Fictional anything is fine in fiction. This is the definition of fiction: fictional things, fictional concepts, fictional characters. If it's fictional, if fits in fiction. Wikipedia has a list of fictional continents, for starters. Power to you!