While I'm not a big fan of plastic anything, I am a fan of repurposing, and a couple years ago I found a use for "cuptainers," (the plastic cupcake containers you get if you buy a dozen cupcakes in a grocery store). These containers make excellent "mini greenhouses" for starting seeds.
I'm attaching a pic showing a square of newspaper, a "cuptainer" and a small juice can. Basically, I cut the newspaper (5-6 layers thick, about 4.5 - 5" square--you can trim it if it sticks up too far), place it over a cupcake "hole" in the container, push it down with the empty juice can, then give the can a good solid twist or two to pack the newspaper into the cup area. Then all you have to do is add moist soil to the newspaper "cups," poke in your seeds and mist the entire container well. Label the container--I use masking tape because these containers can be used for several years--snap the lid shut, and wait for your seedlings to sprout. When you need to leave the container open, just place the bottom of one inside the (opened) top of another. This saves space on your potting bench, porch or wherever you've set the containers. When you are ready to plant, lift out the newspaper "cup" and put it and the plant in your garden. If you don't buy cupcakes (my daughter bakes cupcakes as a hobby) you can purchase the cuptainers online, and if you split the cost with friends or a gardening club, they are fairly inexpensive. And remember, they can be used over and over again. Since they stack into each other, they take up very little space when empty.
Happy Gardening!