An unlimited time contract giving you an "Anmeldung" is already 2 out of 3. The third is the requirement of "ausreichender Wohnraum" (sufficient living space).
The exact square meter number may vary by federal state, you would have to look it up for your "Bundesland", but in general:
A self-contained apartment with kitchen, bathroom and WC is always considered
- twelve square meters for each person over the age of six are available
- ten square meters for each person under six years of age are available.
- Children under the age of 2 are not counted
- The decisive factor is not the living space available for each person, but the size of the apartment including the adjoining rooms.
- A shortfall of around 10 % in the size of this apartment is
"harmless" is a rather weird translation for a weird German wording and means they will let it pass, if it is less than 10% off, because it would be too much hardship to make someone move for a square meter or two.
So it is 2 adults and a three year old kid. So you need to rent something that has a kitchen, bathroom with a toilet and (12+12+10 =) 34 square meters combined. Anything between 31 and 34 might be acceptable, but legally you need 34.
That is not big, I kinda hope you rent something bigger, because in 34 square meters you will feel very boxed in with a three year old. But legally that's it.
Make sure you bring your rental agreement to the appointment. And maybe a "Kontoauszug" (account statement) showing you paid them at least once. The account statement maybe optional, but my rental agreement was so old it was typed on a typewriter and specified rent in DM, the currency we had before the EUR, so maybe it was only me. But maybe not. Just bring it, better to have it and not need it, than to have to make another appointment.