copy from HiNative
Same meaning, but outset would be most often used for a journey or something conceptually similar to a journey. It's a pretty subtle difference, don't worry too much - if in doubt just use "beginning".
From the outset, he had the feeling that it might have been a mistake to enter the PhD program.
From the beginning, he had the feeling that it might have been a mistake to enter the PhD program. (Same meaning, I prefer the first wording.)
I knew it! They were just pretending to be friends, but were really planning to screw us from the very beginning.
I knew it! They were just pretending to be friends, but were really planning to screw us from the outset. (Same meaning, but I think the first wording is slightly better.)
Definition of 'at the outset/from the outset'
If something happens at the outset of an event, process, or period of time, it happens at the beginning of it. If something happens from the outset it happens from the beginning and continues to happen.