I would not manufacture stories. If you feel like you don't have a good story, take something which you experienced, either personally or within a team, and talk about what you would have done.
This way you can still share more about the context and constraints, but you have a bit more freedom to talk in hypotheticals.
Okay, "generating" is a bit of a vague term, so just in case, I'm going to say that you should never create completely false stories for behavioral interviews. There's so many ways this can come back to bite you:
If by "generating" you meant taking an existing story and embellishing it a little, that's totally fine. Behavioral interviews are all about making yourself look good. But do not fabricate entire stories/answers from scratch.
I highly recommend going through our entire behavioral interview course: Master The Behavioral Interview As A Software Engineer
These 2 lessons are particularly relevant:
Will the interview notes/feedback from behavioral round (first round) be available to all subsequent interviewers?
At Meta, every interviewer at least shares the questions they asked with all the subsequent interviewers, but they usually don't share detailed notes. However, it's still possible, especially for more senior candidates.
and will they cross question me about it in the following rounds?
Probably not, but it's possible.
Eg - for driving efficiency if I say I improved the bottlenecks in an ETL pipeline, will the interviewers in the next round deepdive into this? Or If I say I trained a LSTM variant, will they grill me in the analytics round about it?
Anything you say in an interview opens you up to getting grilled about it, especially at FAANG. With subsequent rounds, it's unlikely as asking new questions generates more signal than rehashing prior ones, but the current round obviously will.