Can I put a Blast invitation on a paper slip?

Yes. Write the link short or print it as a QR code with any free QR generator. The slip carries the link; the invitation and the RSVP are in the link.

Do parents need my number to RSVP?

No. They open the link, tap Going, Maybe or Can't and type a name and an email. The reply comes to your host page and your email.

Is it OK to post the invitation in the class chat?

Usually, once. Check the group's habits first; some class chats are for school matters only. If in doubt, ask the teacher or the parent who runs it.

Nobody can tell you. Plan for the Goings plus a couple, send one reminder three days out, and ask the parents you know to reply early.

How to Invite the Whole Class When You Don't Have the Parents' Numbers

You want to invite your child's whole class and you have three parents' numbers. The way through is to make the invitation a link, then put the link where the parents already are: a slip in the school bag, the class chat if one exists, the teacher's weekly email. Because a Blast invitation is one link and guests RSVP from it with a name and an email, the slip can carry the whole invitation and the replies still come to you. Here is the plan, in order.

Make the invitation first, then the slips

Build the invitation on getblast.video/new: pick a design or use a clip of your child, add the date, time, place and a note. When you send it to yourself, you get the link. Everything else below is about getting that link in front of parents.

Four ways to reach parents you cannot text

The school bag slip. A quarter-page with your child's name, "You're invited", the date, and the link written short or as a QR code (any free QR generator turns a link into one). Twenty slips take ten minutes to make. Ask the teacher whether handing them out is allowed; most schools say yes if every child gets one.
The class chat. Many classes have a WhatsApp or school-app group. Post the link once with two lines. Do not post it twice; reply to questions instead.
The teacher's channel. Some teachers will include a line in their weekly email or newsletter: "Maya's birthday party, details and RSVP at this link."
The parents you do know. Send them the link and ask each to forward it to two families. The invitation looks the same however it arrives.

Why a link beats a paper invitation here

A paper invitation with your number on it asks a parent you have never met to text a stranger. A link asks them to tap. They open it, see the invitation, tap Going and type their name and email. You get the reply without ever exchanging numbers, and the parent has the party details in the invitation whenever they need them. It also means the slip can be small, because the invitation does the talking.

Things to put in the note

"Siblings welcome" or "Just the classmate, please": say it, or you will get both.
"Drop-off" or "Parents stay": parents of five-year-olds need to know.
A reply-by date a week before the party.
Allergies: "Tell us about allergies in your reply"; the RSVP has a note field.

What to expect

Whole-class parties get replies in two waves: the parents who know you, within a day, and everyone else in the last three days. Send the link once more three days out, through the same channels, and count on a few who never reply at all. Plan food for the Goings plus two.