How new construction gets assessed, and the partial first year
A house completed mid-year is assessed for the part of the year it existed.
New construction enters the roll differently from existing property, and the first two years often look strange.
Prorated first year
A residence completed part-way through a year is generally assessed for the portion of the year it was habitable. The first bill can therefore look surprisingly small, and the second — the first full year — arrives as a shock that is not an error.
The lot before the house
Until completion the parcel is assessed as vacant land, often at a small figure. Buyers of new-build homes who budget from the seller's last tax bill are budgeting from a vacant lot.
Class codes lag
A newly built home can remain coded as vacant residential land for a cycle. That matters for comparison: it puts you in the wrong pool.
Unsplit parcels
In a new subdivision the village assigns street addresses before the county splits the parent parcel. For a period your house has an address and no parcel of its own, and the assessment sits on the developer's parent parcel. It is not an error and it resolves, but it means there is nothing to appeal in your name yet.
What to do
Read the first full-year notice carefully — it is the first real statement about your house, and it is built from plans rather than an inspection. Square footage errors are common in exactly this situation.