There are several different stories about the mantle going round these days.

One states that it was made for Willem I's investiture. That must have been his investiture as king in Brussels in 1815 and not his investiture as sovereign prince on march 30th of 1814 in the Nieuwe Kerk in Amsterdam. After that the mantle has been worn by every other monarch. Even though it has been trimmed here and there for queen Juliana (the square corners were rounded off) and some of the stained ermine would have been replaced.

Another story tells that the mantle was first made for Willem II's investiture in 1840. Just like the crown, sceptre, orb and state sword that are still used (Willem I had his set but they were used in Brussels and they were not impressive enough for his son and had bad memories).
Willem III and Wilhelmina wore his mantle but in 1948 Juliana's designer Edwin Dolder thought the velvet was unsuitable for a queen so replaced it with new fabric, putting the old ermine and gilded lions on it. He changed the fastening and gave the mantle rounded corners. In 1980 Beatrix' favorite designer Theresia Vreugdenhil was shocked to find the mantle completely wrinkled and red stains on the ermine. She steamed it ready and cleaned up the ermine. Some of it had to be replaced. For it's replacement she had the use of old ermine coming from an eveningcap that had belonged to a mrs Brenninkmeijer (from the C&A dynasty hence the saying HM is wearing a C&A model...).
Theresia Vreugdenhil did create straps for the robe to stay on Beatrix' dress. That system was not used by Willem-Alexander as the robe hung much lower and wasn't over his shoulders. The exact method of fastening is still unclear to me.