There is no set time but it is a popular route with very limited capacity and few alternative options. Trains being unavailable weeks or even months in advance is not unusual, particularly at busy times.

Summer is peak period for such travel so as soon as you can you should reserve travel on Eurostar services.

As well as the eurail booking website you can check availability and book here https://www.b-europe.com/EN/Booking/Pass#TravelWish

You will need a pass cover number to book you can get that here https://community.eurail.com/mobile%2Dpass%2D62/pass%2Dcover%2Dnumber%2Dgenerator%2Dis%2Dlive%2D5653

Only to add : if there were to have no seats to Amsterdam, there will be a lot more availability to Brussels. From there hourly reservation-free IC train