Like Cheerful M, I honestly don't wait for DD to stop crying. I ignore her and say that she has to stay put and even if she hollers the whole time, as long as she stays on the mat, I let it go. Some people don't start time out til the child is quiet, but I just want her to sit. If she gets up, the timer restarts and I put her back. I don't even talk to her. I might be nearby (like if we are in the kitchen and she's in the dining room) but she doesn't get my active attention. When she's done, I get down on her level and talk to her about her actions and have her apologize to whoever she needs to.
Not everything needs a time out. If she threw a toy, I might just tell her if she does it again, the toy is gone and put THAT up.
For us, the time out is taking DD out of a heated situation or away from a fun thing that she was enjoying before she decided to act up. I suspect she will be like her sister where losing a sleepover will be quite effective.
If she didn't do a time out then what would you do if she threw something at someone? What do you think would work for her? She should do something. What about having to give up the toy? Friend of mine puts contentious toys in a time out of their own so nobody gets them. Or having to sincerely apologize to the offended party?
When they were older than your DD, my SD would watch you picking up the toy and throwing it away and not be phased. But if you told her she could not do some social activity, then you'd get her attention. Her brother would get upset with the loss of toy or loss of allowance. Every kid has something. Figure out her hot button item, but don't let her push yours.