Normally you should be ok, with an official document or international vaccination booklet. 

Please note, that some countries are changing rules (i don’t know for Belgium or the Netherlands). Like Italy, the vaccination is valid only 6 months or in Austria you need a booster to enter without PCR test. This rules apply in many countries for check-in in hotels or to eat in restaurants or bars. 

Thank you so much!

Requirements vary per country, although the COVID certificate has been standardised. You can check requirements via reopen.europa.eu (the best is to click further to the websites of the countries themselves).

Also note that some countries have invented their own names for the EU digital COVID certificate; "green pass” is one of those names.

It really varies per country but you canNOT rely on your home-certificate to be taken everywhere. f.e. mostly IT and FR they DO want to check that QR-code EUR style-PLUS that now quite often they also want you to have that booster injection. In those 2 you also need to be able to show it whilst sitting in trains. Sometimes they check before boarding and will refuse you if they cannot be convinced.

However-other as many foreigners seem to think-the checks are more often for HTL and Restrt-places you probably cannot do without whilst travelling. Plus that for some countries (again IT, also others) you also need to fill out a pre-arrival online statement AND even still a kind of test.

Go to a general touristy site like the forum like on tripadvsior to see how you can get this EUR QR code and how it is done-this also varies an enormous lot between countries.

PS-if you only want to travel in NL+BE then a general EUrail pass is not really worth the money