I have a relatively thin foamy mat from Amazon as well (one which folds). It's not too soft but seems to be fine? Before I just had a blanket on the floor, but he'd always grab it and wasn't moving as freely as he could because of it. You can see if your little girl can do tummy time on floor with some support (roll a little blanket under her chest, or use an incline)
I bought foam tiles off Amazon and then have a mat on top and she’s fine that way.