Since you’ve had the silage tarp down for a few months already the cardboard won’t be a big issue. We did the same. That’s more helpful if you’re starting with bare lawn and does help smother grass or maybe if there are heavy perennial weeds. But one of the most amazing things is how incredibly productive no-till can be right from the start, so don’t think for a second you can’t just plant right into those beds and get some amazing crops right away.