Hi Elgreco and welcome to GoY. Is the manure fresh or well rotted? Fresh manure would burn the roots of the plants whilst well rotted manure should be fine. If you cut slits in the cardboard and weed suppressant then weed seeds that are in the soil could start growing but that is you choice. You could plant out brassicas, salad crops, beans and peas or even tomato plants depending on where you live in the UK.

Think twice about putting membrane in a veg plot. How would you dig up your root veg ? And when it comes to following years how would you find the slits in the membrane? If you cut new slits every year you'll soon have it shredded.Think how may cuts you'd have to make for eg a row of lettuces. It is not difficult to hoe between the rows regularly to deed with young weeds and you'll have to do that anyway even with membrane as surface weeds will still grow above the level of it..

Not sure what you mean about the membrane doing its job. The purpose of it is to prevent the growth of deep rooted weeds.
Its purpose is not usually to kill off weeds that are already present.
Manure should normally be dug into the plot early in the season.
Sorry to sound negative, and sorry too that this doesn't answer your question- just pointing out a few things you might like to consider before committing yourself.

Maybe I'm wrong Stera but I read this question as putting the cardboard and weed suppressant down just for this year...

It is a pity you did not plant potatoes in the area. That would have cleared a lot of weeds and given a crop you could use. The manure would have had to go beneath the potatoes. You should not need cardboard and weed suppressant. One or other would do and I agree with Stera that weed suppressant membrane would not work on a veg bed but if it is only for this year then it is an expensive choice. I do not like membrane in any situation because weeds can grow unnoticed until they are a real nuisanmce to get rid of.

MG Elgreco does mention actual membarne, which is a bad idea for a veg plot.

I still think it is only for this year... so not necessarily a bad idea, not something I'd have done myself.

Just imagine digging it all up again at the end of the season...

I 'think' it is on the top of the soil, not buried but unless Elgreco responds we've no idea!

Its so frustrating when you want to help but the questioner doesn't come back. I don't honestly think this plan is going to work very well. Digging weeds out of a small area at a time and planting that would be a better option for me. If the cardboard is laid on top of the soil it will probably still be there when the membrane is removed. If the manure was well rotted it would be better dug in. You can't really get away with making a new bed with no digging at all.

Well you can Stera, at least folk do, but I wouldn't try it!

So sorry to take so long replying, please forgive me. First off I have done this before to clear ground for a piece of lawn, and believe me the membrane does not hinder the worms from dragging the cardboard down.
Moon grower, you are spot on, it is only a case of clearing the ground for next year.
What I was after was suggestions as to what I might plant through slits so as to at least grow something this year.
By the way when I used this method before the soil was absolutely sublime.

See my initial response Elgreco where I give suggestions of veg. you can grow.