For youth 12-18 years old, there are indeed day passes available:
https://www.ns.nl/en/featured/jongeren-dagkaart.html
From 19 years old, there are no day passes for the train available.
For the travel you mention, an Interrail pass will be too expensive. You could however consider a 1-month Dal Voordeel subscription for 40% discount during the off-peak hours:
https://www.ns.nl/en/season-tickets/
You'll first need to order a personal chipcard (then click on the link for the contact form), and when you've received that card, you can order a subscription at an NS ticket office or by phone; in the latter case, you'll need to load it onto the chipcard before you can start using it. After 1 month, you can stop the subscription via your NS account (= change the subscription to the free NS Flex Basis). Payment of the subscription and the journeys is via monthly direct debit from your bank account. Your bank needs to accept SEPA direct debit for that to work; alternatively, you can get e.g. a free Revolut account which will allow that.
The costs of the personal chipcards can be reimbursed via NS customer service after you've ordered a subscription, because the chipcard is included for free with it.
Alternatively, you can tap in and out with a contactless payment card, but then you'll always pay the full fare.