My 3 year old just started childcare a week and a half ago and she’s been okay so far.
Could be that your little one just wants to stay a bit longer and play!

My son is the same. As soon as other parents come to pick up their kids he starts getting upset and then cries when he sees me. Gets over it quickly though

I agree it could be different things;
maybe she missed you and just gets emotional seeing you
maybe she had fun and doesn’t want to go yet
maybe she’s overtired and overwhelmed
How is her behaviour prior pick up time ?
I would have a chat with the staff and brainstorm if there’s anything you could do to help her

It could be that your toddler is having so much fun with the other children that when you arrive she doesn’t want to leave. Does somebody else sometimes pick her up? If so you could ask if she does it with them too. How often does she go to Daycare? Does she normally have a sleep during the day at all? Maybe she isn’t getting enough. If she has cut out day sleep completely perhaps try getting her to have one on alternate days. It worked wonders with one of mine.