i love fresh herbs too,in India however fresh herbs are limited to cilantro,mint & curry leaves,but i have an acquired weakness for herbs from other countries & so have to grow them from packeted seed,they do well in pots & take about 7 to 10 days to germinate,i grow them outdoors till summer which is fierce in our part of the country,then thay are moved to shady spots in the garden.Unless the weather is cool ,i dont think plastic wrap is needed,but using it will do harm.Happy cooking with fresh herbs

You should see sprouts in about a week. I have had good luck without using the plastic wrap. Most herb seeds sprout easily so you don’t really need it. Make sure the plants have plenty of light and you’re all set!

you are doing just fine and if you decide to put plastic wrap over the plants it would make like a green house effect. just make sure to poke some air holes in the wrap.
you should see “green” in about 10 days

Congratulations on your new garden!

Plastic wrap might help, if the temperatures are starting to get cool or even cold. But be careful: You don’t want to cook your little seedlings. Germination usually occurs within 7 to 10 days. There should be something on the seed packets.

Good luck!