No, that's not right, not at all.
By contrast - DS is 2.5, just started at nursery, 3 mornings a week. To my astonishment, he seemed to hate it (I couldn't get him out of there at drop off with DD over the last year, hence my surprise).
His key worker spotted us as soon as we came in, she'd come over, get down to his level (him clinging to my leg,crying, most unlike him) - ask how he was, how was breakfast, did he enjoy his snails on toast? That sort of thing. Then she'd have left a small bit of setting up to be done and say,'right, DS, the dinosaur table is nearly done but I need your help to put up this poster on the wall/ find all the dinosaurs with long necks' etc. Total distraction technique.
We are a month in and he now runs through the door, straight to a table to start playing. I get a kiss and a cheery wave. He even wears his nursery jumper. He's developing an affection for staff and they are helping him to enjoy his time there.
That's what good, child-centred nurseries do. I'd report yours to Ofsted simply because they don't seem to be supporting the children's emotional needs.
I'm sure you'll find a better place.