"Let alone __" is an Idiom. Its used after a description of status to show how far away another status is.
If someone asks a high school student, when they are getting their masters degree; That student could say "I am not close to graduating high school, let alone close to graduating with a bachelors".
Idioms are hard to place in a nice neat container sometimes, Im not able to say with confidence its a particle phrase, but i know its not modifying we.
Let alone _ is both describing how unobtainable the state, or status is while also saying what part of it is unobtainable. That state being "whats happening right now."
To put it anther way, enjoyment of "whats happening right now" is unobtainable by "we" because "we" has yet to experience "Whats happening right now".
Since the state "whats happening right now" is described as unobtainable, a person could reasonably say that let alone is a participle phrase.
I hope that helps.