When you SAVE your game, you save your PROGRESSION: The Witcher 3 saves your character progression (inventory, unlocked talents and perks, what perks you use, the recipes you have unlocked), story progression (the quests you've completed and what choices you've made) and your map progression (what locations you've visited, what nests you've destroyed and what fast travel points you've unlocked). Note that these are things that the game already keeps track of for purpose of checkpoints and autosaves, so it's likely that the game just has a record of what happened so far and stores that in the RAM memory. When you then save, that record is formed into your savedgame.
When you LOAD your game, the game loads a WORLD STATE. The Witcher 3 starts with a world like the one you get when first starting the game: Geralt has literally done nothing. Then, that game record that forms your savedgame is applied to the game: every quest you've completed, every dead named NPC, everything you have or haven't looted, it's all applied to the world and Geralt. this is a large part of the loading time. While Dangerzone says the game needs to load shaders and stuff like that as well, those are actually loaded BEFORE you even get to the main menu, because that main menu has an ingame Geralt visible with all visual bells and whistles already applied.
To give an example of how detailed this loading process is: Geralt's beard grows dynamically based on how long since his last shave. So when you load the game, Geralt's beard length is calculated and applied to his model.
The reason the game starts from a basic world is because it's a massive world and everyone plays differently, so everyone has a different savedgame file, but you can't save the entire world because it's FAR too big. Imagine you're a tailor known for custom-fit pink shirts. You can't possibly have a closet somewhere in your workshop with a copy of every single shirt someone might buy. Not only would that take a monstruous amount of time, but it's likely that there are certain extreme combinations of customizations that barely anyone will ever have need for and thus would only take room in your closet. Instead, you have a few pink shirts in every size from XXXS to XXXL and take a list of measurements from your customer, like their gut size, their chest size, their arm length, their neck size,... You then use that to choose the proper base size and make some customizations like taking in the girth, or shortening the sleeves,... to make it fit your client better. Similarly, The Witcher 3 takes the base map (or maybe chooses between a few base maps depending on your progression in the map storyline), fastforwards all the quests so people are in the right place with the right dialogue set up, then places you in the location you left the game. Obviously, fastforwarding through alll that content takes a while.
The Witcher cannot keep the entire game in memory at all times, because that's just not possible. On my PC, the Witcher is 32.5 GB of hard drive space. A PS4 has 8 GB of memory, and about half of that is for Playstation OS. You'd need a beast of a Windows machine with about 40 GB of memory to hold it all at once.
An SSD won't help much, because as mentioned above, most of what happens is done outside of the long-term storage. Loading and processing the world state, creating the world itself, spawning the enemies, drawing the textures and models,... all of that is done by the processing hardware, like the CPU and GPU. Once it's in the RAM, the SSD doesn't change anything.
If you compare that to a game like Super Meat Boy (to give an extreme example): SMB saves are just a bunch of boolean flags and times, since you can't save in a level: your level times and what you've unlocked. You also load on a simple static display that likely is prerendered. The level generation itself doesn't even happen until after you select a level. But if you add all the loading times of a level together, you probably have well over a minute of waiting. But because the loading is staggered, you don't notice it.