Question about shoes/socks (gap mainly)

I can't keep shoes or socks on my kid. She kicks the shoes off and the socks always seem to fall off.

The gymboree socks stay on, but they slide down so that the heel on over the arch of her foot. They're size 6-12months. I thought maybe she just needed a size bigger at first, but I started using these at 3 month and had the same problem.

I bought a bunch of Gap/Old Navy socks and she literally crawls right out of them. I can't decide if they're just too big (which I think is the case) or if her foot is just too narrow.

As far as shoes go, we've tried crazy8, gymboree, adidas (shell toes), ralph lauren, gap, and a couple other brands. None have stayed on. May plan was  to use shoes to keep her socks on, but it's not happening.
I haven't tried robeez.

 Any suggestions?