I've already explained the technological progress using our own history. In addition, the First Order is partly the remnants of the Empire. So they already have the technological know-how of building a Death Star. Further, as said in the film, there are unknown and unexplored areas of the galaxy and in fact, I believe the First Order set up shop in those unknown and unexplained places. So it actually makes sense if you gave it some thought.
People who think there should be as much technological progress as in our world and times or any at all have cleary not understood the StarWars universe. This is a galaxy where the Republic has stood for thousands of years, where hyperspace travel, blasters, lightsabers, holograms and targeting computers have been around for thousands of years.
You should not expect any technological progress in 20 or 30 years.
Starkiller base is also not a direct technological progression at all.
The mass alone you would need to accumulate for something like this, you could probably build like 10 Deathstars easily. Nobody noticed?!
The Emperor had the plans for the death star during AOTC times already and Death Star II was just a slightly bigger and more powerful copy of those plans, like 25 years later. (and took multiple years to get to semi completed state).
Starkiler base is a planet with an atmosphere, trees and birds. HOW DOES IT MOVE THROUGH HYPERSPACE and maintain the atmosphere?
(EDIT: Also IF you can build up planets and move them around through hyperspace as a small splinter faction in the course of like 10-20 years, wouldn't that universe be full of artificial star systems? You could essentially just reconfigure systems how you want. A cold rocky desert world? Just move it closer to its sun! No problem. There would only be perfect worlds in such a universe. It just destroys so much of the lore.)
It also uses a completely different method to fire. It sucks suns empty for ammunition, something the Deathstar managed with its own reactor core and then fires 5 weirdly arcing and homing beams to destroy multiple planets at once. It is a terrible concept.
They could have just used a Death Star III that shoots at a sun and causes it to go Red Giant that engulfs its orbiting worlds but no, they went with the more fantastical "let the dark side suck in all the visible light" rhyming metaphor and imo it is absolutely impractical and terrible and not a direct technological progression.
It also makes no sense that the Resistance, after a brainstorming session of 2 minutes knows exactly how to blow it up with 8 X-Wings, when Death Star I and II both were practically invincible and could only be destroyed in last ditch efforts after construction blueprints were found or before the station was fully operational.
Starkiller base IS fully operational and it is still a cakewalk to destroy it. It invalidates the efforts in ANH and ROTJ.
The whole thing feels more like the script writers didn't really care for logic or lore (it is a space FANTASY!) and said "let's have the final lightsaber battle in a snowy dark, cold forest and we need a trench run! Where? Could we somehow combine the superweapon and this location? Yes! Let's do it!"
