Frank Herbert's Dune was published in 1965 and it's still a perfect entry point to science fiction without being overwhelming. The difference from what's probably worrying you is that Dune doesn't bombard you with technical explanations of how everything works - Herbert builds the world organically, like it's just another planet you discover as you move forward with Paul. It's politics, intrigue, a bit of mysticism, and a well-thought-out universe without having to memorize spaceship specs. The pacing is excellent, it hooks you fast, and mentally it's not that different from reading epic fantasy.
Another option that would work for you is Isaac Asimov's Foundation, way shorter and more accessible than Dune. It's almost more of an intellectual thriller - it follows a group trying to preserve civilization using psychology and history. There's not much intimidating technology in the background, it's more about ideas. Science fiction sometimes scares people because it seems like you need a master's degree in physics, but Asimov shows that it's really about human stories that happen to take place in the future.
My advice would be to start with whatever appeals to you most - if you're into epic politics like Lord of the Rings, Dune is your spot. If you prefer something more fast-paced and conceptual, Foundation. And here's the important part: don't be afraid to drop a book halfway through if it's not grabbing you. After years of reading different genres, I've seen a lot of people feel obligated to finish classics when really science fiction has too many options to waste time on something that's not actually hooking you.