Do you want to have babies? If so, you can hang up a nestbox. If you see either of the parents going into the box, you can move the egg there.

O don't think I have much of a choice anymore

Will they still take care of the egg if I take it out of its place?

Cockatiels are very good about following the egg if it's in a place where they feel comfortable. They'll probably like the nestbox better than a place on the floor.

Be sure to put 2 to 3 inches of bedding in the nestbox. Clean wood shavings (not sawdust) are best. Aspen or pine is good, don't use cedar.

Forgive me for asking, have you bred before? Hopefully everything goes smoothly!

this is incorrect guess! I made the same mistake and still dealing with consequences! There is always a choice. Don't make the wrong one.

An egg just hatched today (or yesterday night), and I realized the chick was far away from Barbara, I picked him up with a towel and put him near her. She shook him and threw him. I decided to leave them. Later, I saw the chick on the cold ground again, so I put him back on the towel.

I don't know what to do. Should I hand feed the chick? Or should I leave it to them? If I do have to hand feed him, what should I give him?

I think it would take a lot of experience to hand feed newly hatched baby, because of the size. I hand fed chicks at about 3+ weeks old, and it was still challenging, but they were much bigger!
The egg should have been in the nestbox. Her attitude probably resulted from not having a secure place to have this chick. Where did they incubate? what about the father?
Also, you need to feed the parents soft food so that they can safely feed the newborn.
In my opinion, the set up didn;t allow the parents to feel safe about having this baby, and their hormones are way down by now to feed her.
Poor baby I think her fate is predetermined, you posted a day ago, sorry I just saw this.
I m no way an expert...

You feed baby bird formula to baby birds. But it's a complicated process.

Erik, any update?