Is this spacing too close?

I simply scattered the cosmos seeds directly in the soil. Now the seedlings seem overcrowded – they appear so thin and delicate that I'm unsure if they can survive being lifted and transplanted. What would you recommend?

My preferred planting method!

If you want you can try to lift and transplant though how would Mother Nature do this?

Are you intending to leave them in the pot or grow them in the ground?

You can, for instance, pull that whole plug of soil out, break it into four quarters and repot (or plant out). Sure, the ones right on the fracture line will die, and if the roots are long enough, you might damage some others when separating, but you have enough there, that some will live in each of the four new plantings.

Sometimes I'll pull the plug out and then carefully tease them apart with chopstick, keeping everything damp as I work, and then repot individuals. But that's a lot more work.

Cosmos are big plants, and need a decent amount of water in that they aren't drought tolerant.   They do best in the ground or a large pot that is kept damp and mulched with at least 2" of mulch, wood chips, law mowings, etc.  Recommended spacing per plant is 12" to 18" or 30+ centimeters.

If you want to transplant them, and their roots are tangled, put that whole clump in a bowl of water and let it soak away the dirt , tease the dirt  away until the roots are exposed.  Work in a shady location.   It's called root washing.  You can do it wth transplants bought at the store where there are several little veggies in a small container.  Have enough larger pots filled with soil and ready to go to put them into.  More will survive than if you pull them apart in a dirt clump.  When those plants get as tall as your middle finger they can be transplanted into their permanent location.  

Not even sure how you'd keep a little container like that watered with even one plant in it.  The roots will fill it and dry out quickly.