There's a previous FP on the subject, with more answers.
The key herb in traditional za'atar grows wild, is endangered and not commercially available.

I love to toast my sesame seeds just a little bit before grinding everything up.

Many za'atar recipes use just one of the herbs Amanda mentions (thyme, marjoram, or oregano). But almost every writer who provides a recipe for this spice blend makes it clear that cooks concoct their own variations, so you should feel free to start with small quantities and play around with whatever suits your fancy, from ingredients to proportions.

Thyme, marjoram, oregano, sumac, sesame seeds, and salt.