Is this possible to load a saved game faster?

The cutscene is masking loading. It is not waiting to start, they are just giving you something pretty to look at. When the cutscene ends, there is nothing more to show you so you see a traditional loading screen.

To explain the difference in save vs load times (a few seconds to 1 min+), think of what is being loaded vs what is saved:
Load: Lighting, character models, inventory, other assets of the world (terrain/scenery), etc.
Save: Inventory, dialogue choices you've made, etc.
There is no need for the game to save all of this scenery and other assets, which explains the much shorter load time. Of course, some of these are similar (inventory will be saved/loaded for example).
Loading elements of the world does not happen only one time, from the main menu. As I mentioned in my comment, that would take a huge amount of time, and it's much more efficient to load/unload assets dynamically. I may be lacking the technical knowledge for this next statement, but I don't think it would be possible to load everything the game requires into memory at the same time (especially on a PS4).

That aside, there is nothing you can really do to actually speed up the loading from a system point of view. I suppose you could invest in a SSD, but I am completely unfamiliar with how those work with a PS4, as I do not use one.

In regard to the scene playing before the load bar shows unfortunately you can't disable it on anything other than pc via a mod, Through testing with and without that scene no it doesn't mask loading at all it's just there as a recap from what i can gather.

Load times are affected by the size of the save file itself. (e.g. Your near the start of the game save file is less than 1mb load time is roughly 1 second, but later on when the save file becomes 1mb+ it tases longer and longer).

I have a save from early on with mod to disable the recap scene and load time is 1 second, my current save file is 1.3mb load time is about 5-10secs.

Tested with both pc and ps4 graphics change a lot from ps4 to pc but the load time is the same. Tested with ps4 but timing after the annoying scene.