In the English Vocabulary Profile at C1,
‘in no time’ means ‘very soon’
A search for collocates in THE MOVIE CORPUS:
1 AT 138
I know this is a big change for you, but it‘ll feel like home in no time at all.
2 FIXED 29
Never fear. We‘ll have Alice fixed in no time.
3 FEET 25
4 NORMAL 14
5 FLAT 12