As I understand it, the seed sprouting consumes chemical energy from the seed to grow, but there is only a limited supply. When the energy of the seed runs out, if the plant can't collect energy from sunlight on its leaves, it will perish.

cardboard mulch interferes with water and oxygen movement and is bad for soil. I would just remove it.

I'm afraid you can't have it both ways ;-) Either the cardboard stops plants growing through or it lets plants grow through. That applies to weeds and your seeds alike.