Healthy seedlings: It’s not too late to warm up the vegetable patch, with compost, or layers of newspaper or cardboard. Leave it for a few weeks until your seedlings are hardened off enough to plant out, or buy plugs which will already have been kept outside before going on sale.
Don’t be bullied by the conventional gardening industry that says you have to wreck your back and try your temper by digging the whole plot at once, and then mass planting to fill all that bare space before the weeds take over!

You can leave it til end May or early June to put out seedlings. They’ll soon catch up, and meantime the worms will be working for you under that warming mulch until you are ready.
Move aside enough mulch for the seedlings you want to plant. I prefer patches of plants to cover the soil rather than rows (Nature usually doesn’t leave the soil bare; the ground is usually colonised by seedlings, or covered with last years leaf drifts, or decayed vegetation. Being too tidy exposes the soil to erosion)
The mulch will have smothered most of the weeds and the soil will be alive with worms, aerating the soil for you. No need to dig or fork the whole plot.
Do a bit more loosening with a hand fork, just enough to give the seedlings easy penetration for their roots, water them in and take care of them as usual. Maybe a few organic slug pellets, and some twiggy branches to deter the pigeons, and in my garden just now, a pair of ruthless starlings…