Is it normal to want your ex back?

Cautiously... and only if things are right,

Key question: What caused the split. What mistakes were made on your part - and are you willing to really change? What about your behavior has been improved?

You can inquire if she is interested in possibly patching things up. Be prepared to move on if she says no.

Be prepared to work out issues and perhaps go to counseling together as part of the process to assist the two of you to figure out the causes and allow you to change things.

I wish you well with this.

Normal to have feelings, not normal to want to call her

That goes to show how weak you are. Grow some balls.

It's always possible to try.
My ex reached out to me after about a month and we didn't get back together but we were very good friends for as long as it was possible.
Sometimes you can get back together as well, if the timing was just wrong before, but after only a month nothing has changed probably.
It's impossible to give advice without details.

Depends in why you broke up in the first place

You can try. But if you don’t hear back, you need to drop it.

Just leave her be!

Allow yourself to feel the pain. One month, the wounds are still raw open and you want her back because you no longer want to deal with the unpleasant feelings. Don't chase those thoughts, they'll just go away. Give yourself time.

She's probably moved on, not really much of a point.