Growing your own thyme is a great idea, it grows outside maybe you can put the pot on the windowsill, dont over water it as it needs a slightly dry soil, and you are good to go. The small grey-green leaves will be grown on clusters of thin stems that will bring the fresh aromatic thyme flavor straight into your dishes.
Remove the plastic bag is the first thing to do. Keep the plant indoors, not fully exposed to the sunlight. Make sure you water the plant every second day or whenever it looks floppy. Water deeply at least once a week. The best practice it is to transplant to a larger pot. It keeps the roots growing deep and the soil moist. Your goal when growing in a container is to keep the soil from drying out. The best time of day for water is early in the morning. One last tip if you keep them in a pot is to have a flowerpot dish that he's keeping the soil moist and at the same time, allows the water in excess to drain