The initial wavefunction may be completely determined by the laws, and under MWI that's all you need.

Bundling the initial state into the laws of physics seems like a confused way of looking at things to me. The state and the laws are different things - if you muddle them together conceptually, your accounting is likely to get equally muddled. Also, most of the rationale for the size of the "laws of physics" being small evaporates. The initial state might be enormous, for all anyone knows. The laws of physics could be infinite too - but there the hope that they are small and finite seems slightly more reasonable.