Thank you for the suggestions. I'm afraid that it doesn't accurately convey my meaning as I want to sound more strict: at the time of it, not to wait until morning comes to know that now is the time... Does that make sense?This isn't idiomatic; in fact it sounds like the title of a 19th-century poem - by Wordsworth perhaps? Try:
When it's morning in Europe.
When it's morning by European time.