Also Dr. Klein writes the following about it:
Applications for Baukindergeld amounting to a total of 4 billion euros, and thus 40 percent of the 10-billion pot, were used up by mid-February 2020. Baukindergeld can be granted for a total of 833,333 children; it has only been applied for 333,333 children so far. KfW does not communicate exact payout numbers. It only states that everyone who is eligible and submits complete documents will receive Baukindergeld.
That means 40% in one and a half years. So it should still be possible.
Of course, it is better not to count it in and to be happy about an additional, "unexpected" sum.