One of the wonderful things about improv is the possibility of starting 'in the middle'. Del Close used to say, 'start in the middle of a scene'. Have a history that led you to this point. Agree on what came before, allow it to evolve through the character relationship.'
'Beginning in the middle' is sort of the way I felt years ago about Rosh Hashanah. As a society, we celebrated the New Year January 1st, one week after Christmas. But Jews celebrated the New Year toward the beginning of the fourth quarter of the year.
For kids, that felt more 'right'---since the end of summer signified the beginning of a new school year, and that 'felt' more like a 'beginning' to me. So, Rosh Hashanah seemed appropriately placed for me in time.
The same with an improv scene--- you can begin in the middle---that will feel right at times.
And here is a link to Del Close notes I provided for the Applied Improv Network folks: DEL CLOSE NOTES and read the first few pages to enjoy my own Rosh Hashanah story that includes a workshop with Del Close.