I was wondering how hard would it be to create a neanderthal? What problems would be encountered?

So the first problem would be we need DNA which we do. We already sequenced the DNA of neanderthals. https://en.wikipedia.org/wiki/Neanderthal_genome_project
So we must have some DNA
Next we could create the egg by https://en.wikipedia.org/wiki/Somatic_cell_nuclear_transfer
then just inject it into a human woman
Would it be that easy? Why dont we do this? Wouldn't there be alot of good science that could be created by doing this?