Learn Dutch: Duizenden vogels: het aantal is niet te tellen. - Thousands of birds: the number cannot be counted.

For indefinite large numbers like hundreds or thousands, Dutch simply adds -en to the base number to create aggregates: honderden (hundreds), duizenden (thousands), and miljoenen (millions). The suffix -tallen is mainly used with smaller numbers like tien (tientallen = tens of) where just adding -en (tienen) would usually refer to the digit ten itself (like playing cards or grades) rather than a rough aggregate quantity.

How does is niet te tellen translate to "cannot be counted"?

The Dutch structure zijn + te + infinitive is a passive-like construction used to say that something can or must be done. By adding niet, it expresses an impossibility. So het aantal is niet te tellen literally translates to "the number is not to count," which means "the number cannot be counted" or "is impossible to count" in English.

Could I use het nummer instead of het aantal to mean "the number"?

No, that would be incorrect here. In Dutch, het aantal specifically refers to a quantity or amount of countable things (like the amount of birds). Het nummer is only used for identification or ordering, such as a phone number (telefoonnummer), a house number (huisnummer), or a track on an album.