tere are good explanations for most of them anyway.
There are explanations now that we’ve had ages to ponder them. Conversely, the novelization for TLJ isn’t even out yet.
The TFA novel straight up explains how the Starkiller beam could destroy a planet on the other side of the galaxy from where the base itself is located. It just depends on it you want to accept that explanation.
That is to say, you like the movie or you don’t, and that’s your choice. But holding ST and OT up to different yard sticks isn’t exactly fair.
We shouldn’t need novelizations to justify the events of a movie.
But as for different yardsticks, the Death Star was a moon sized space station with essentially a big version of a blaster that could blow up rocky planets. It required the resources of a galaxy-spanning empire to build.
Starkiller Base is a piece of construction many times larger than the Death Star, with a primary weapon requiring seemingly universe-breaking technology that has never been previously hinted at or explained, built by an organization that by all indications is a fraction the size of the Empire.
These are not two yardsticks.
Iteration is your answer.
The German Empire was defeated in WWI, the Nazi’s “rose from the ashes” and 20 years later the Third Reich invaded Poland and WWII began.
The engineering iteration upon the previous weapons, saw the war machine now employ cannon that could span the English channel, unmanned V2 bombs, U boats, and any number of other more advanced hardware (including ultimately nuclear weapons).
Pretty obvious that the First Order is based upon the hardware of the Empire (TIE Fighters, Star Destroyers, Stormtrooper armour, Starkiller Base, etc), and so iteration is your answer to why they are more advanced.
But that still doesn’t answer the question of why they were able to build a far more ambitious project with far less resources. If we saw that they used a robotic workforce and had a lot of automation for their fleet it would make sense, but we get no indication that it’s different from the Empire in this regard. Hux even says that it’s a machine ‘that you have built’. Yet another missed opportunity if you ask me.
Why do we need to see the First Order’s means of production? The only time we saw that before in Star Wars was in one of its most infamous scenes (“Shut me down, machines making machines”). We have no idea how they or the Empire did it so why should it matter?
In the OT trilogy there was no issue showing means of production, since the largest structure we saw was a part of the story’s table setting exposition and they never made anything more impressive than that.
For the prequels, we got a lengthy scene showing the creation of the Clone army, a scene of the droid factory (which was largely unnecessary since the droid army was also established at the beginning of the prequels), and in just GL’s prequels we got an explanation for how the Death Star was designed and saw it being constructed 20 years before it would be finished.
Say what you will about the prequels, it’s undeniable that they have enough rock salt.