Sow grass in March or wait?

Cardboard becomes heavy at 500 sqm2 :)

It annoys me a bit now that it is not done with the filling 1 month later.

Does it actually help to go over it with the rake once a week to minimize weed growth?

Just accept the weeds. Most will go away on their own if mowed regularly. Currently, sowing probably won't bring much. The soils are still cool and the nights cold. It doesn't help much if you get 15 degrees during the day. See it as a chance for the soil to settle a bit before sowing. If you happen to have a cistern, watering can help with this. Before sowing, only loosen the surface with a rake and smooth out any holes/bumps.

Cardboard gets heavy at 500 sqm :)

The packaging from the furniture Swede easily handles that. Don't you also have to buy furniture? :D

It's already been half a year, the furniture is worn out.
Yes, definitely, and after a mild breeze I have all the neighbors at my door.

I would sow now, the prospects are quite good and you can still overseed in certain spots. Better than giving the weeds 4 weeks now. You have to expect weeds anyway, I personally hardly do anything. I only pull out thistles and occasionally dandelions and the rest can stay. Bumblebees love clover, walking on moss is wonderful.

First question would be, what does it mean that you get topsoil and it is smoothed out? Does the excavator come and scrape it off? That has nothing to do with fine grading yet. You will still have to do a lot yourself with a rake and shovel. And if the "topsoil" (a lot of junk is also sold as topsoil) is sticky, you can forget about it without putting something loose on top.

But to the original question: we are in the sunny southwest and sowed at the end of April. That worked well. In my opinion, March is too early, you need a soil temperature of >10 degrees.