Two Sizes Too Fast

As many of you already know, my kids play baseball on local Little league teams. Baseball season starts at the end of March. So in March we had to buy new uniforms, cups, cleats etc...
In March my 7 year old wore a size 13 shoe. This week he told me those shoes were too small. I didn't believe him. I just bought the cleats in March. I helped him put on the cleats. Yup. They were too small.
I went to the laundry room and found a pair of size 1 cleats that a friend had given us. His foot wouldn't fit in. I loosened the laces and tried again. It was like trying to squeeze the wicked step-sister's foot into Cinderella's glass slipper. It was not going in.
March! I just bought him cleats in March. He can't possibly need new cleats now. I was hoping that he could at least make it through baseball season before I would have to buy new cleats. But the season is only halfway through.
Can he really grow 2 shoe sizes in less than 2 months?!