Will tomato seeds grow through mulch?

Or rather, how thick of a mulch will they grow through, in your experience?

I want to keep moisture in the soil around them, but I also want them to be able to make it through the layer.

My mulch options are fresh mowed weeds (not to seed yet) and good old straw.

Technically I have newspaper too, but I'd prefer natural.

This season I started a new bed. (Clay 'gumbo' soil under lawn previously.) Removed grass last fall and covered with leaves and grass clippings. This spring I put down 2 layers of cardboard and about 4 inches of shredded leaves; and saturated the ground. 12/12 plants came up but some were sickly and need fertilizer to make it. When you plant, punch a hole in the cardboard and pull back a marble sized area of the mulch where the seed goes in. The plants will come up fine.

Tomato seeds are small, so they don't have enough stored energy to push them several inches toward the sun, like a bean does. It would be best to let them germinate and get a few inches high, and then carefully mulch after thinning. Leave a little bit of room around the stem..

Cutworms might enjoy the cover that mulch provides. Damping off is also a problem with young tomatoes. Mulch immediately adjacent to the stem can make this problem worse.

Until last year I had volunteer tomatoes coming up through mulch. Last year I mulched very heavily and had very few volunteers but it was good for the Grapevines.