Baby wakes up too early in morning

We have to get to daycare pretty early so I wake her up at 545am. Past few weeks she wakes earlier, sometimes even 400am. I read that we need to sleep train her until her normal wake up time, that if we pick her up when she wakes early she may wake earlier and earlier...!? It’s not working. Her day naps are not the greatest either so her bedtime can be as early as 620pm. I’m thinking a later bedtime is the best solution but with the crap naps she never make it. Anyone with any ideas? The poor thing needs this sleep since she naps so poorly at daycare.