The yolk (used directly in the embryos development) is generated during 10 days (https://www.purinamills.com/chicken-feed/education/detail/ho...). This could give the opportunity to pack a lot of "indirect information" to be used by the future embryo.

Regarding "teaching" the child while in the womb, it is exactly what is happening, see: https://www.americanscientist.org/article/baby-talk

I do agree that some organisms will transmit more "information" (via multiple ways, chemically, mechanical, etc.) than others (like maybe the birds) but the fact is the DNA is just a part of the development process and even if maybe it is "the first one", it will not "pack" everything.