Hi< Mellany, welcome to the forum!
If I wanted to fertilize a no-till garden I would use compost tea.
There are several ways to make compost tea and probably everyone has their favorite.
Here is an easy way:
https://permies.com/t/53922/composting/Compost-Tea-easy
If I wanted to use manure I could make a tea similar to making compost tea or use it as a top dressing.
I don't use cardboard, most folks use chop and drop as a means to keep weeds from spreading. Just chop before the weeds go to seed and let the plant add nutrients when dropped.
I am looking forward to hearing how others do no-till and fertilize.