I don't think there is one date for all. Some countries like the UK have a dedicated recruiting season (aka milk round) with deadlines clustered around Sept / Oct / Nov, and other countries like Germany recruit for everything (incl. internships) all year round.
Back then I made an Excel with all the firms I wanted to apply for incl. their start dates and deadlines and my progress in the application process - if you want to be throrough, I would recommend that sort of systematic approach. You then gotta spend some time looking up the individual dates though!