Well no... required means required. Either you won't be able to get to the platform (ticket barriers) or expect a big fine onboard (100-300€, it's like travelling without a valid ticket). You could also get thrown off the train at the next stop.

In short : it's pointless to try. Eurostar Red (the now defunct Thalys) also has a passholder quota so trains tend to sell out a few days or even weeks in advance.

There are however reservation-free or cheaper (but slower) alternatives.

Amsterdam - Brussels : hourly IC Direct. Reservations not possible : hop on and sit wherever you want. Less busy at train ends.

Brussels - Paris :

Option 1 :

- IC Brussels - Tournai - Lille-Flandres

- TGV Lille-Flandres - Paris-Nord 10€ (always available on the day)

Option 2 fully reservation-free :

- IC Brussels - Charleroi

- R Charleroi - Maubeuge

- TER Maubeuge - Paris-Nord