Eurostar try to stagger the times to minimise overcrowding at the terminal as much as possible - get there too early and you're there before the people who have come for the previous train(s) have cleared.
The tickets will tell you how early they want you to be there. Last time I travelled mine said 45-60 minutes, I'm going again next month on the same service (11:04 from London) and the ticket says to arrive by 09:49, so 75 mins before. Curiously, the one I've booked for July says, for the outbound leg from London, "Please arrive at a kiosk in the station at the time indicated above", rather than the usual "Please arrive at the Eurostar departures in the station by XX:XX local time". The only times "indicated above" are the departure and arrival times - if anyone takes that literally it would cause them problems! The return leg says to arrive at 12:01 for a 12:56 departure from Brussels, so 55 mins.
Back on topic, I would have no worries at all about arriving at 0559 for an 0704 departure.