Two important things.
Plants like warm feet. If you can get the soil warmed, they will do better.
Empty soda bottles (3 liter) work really well as caps. Just cut out the bottom. You plant the seedling and pop a bottle on top of it. If you feel you need the top, it is too cold to plant.
I’m thinking that the cold frames would help warm the soil better.
But I’m talking about starting in late April or early May. The soil is generally warm enough at that point, it’s the late frosts and freezes that are the problem.
It doesn’t sound too early for some, but would give us a month on the growing season.