So, how long before I can take my DNA "ROM" file and boot it in an emulator that would allow it to grow?
What if you could take the (binary) data file of your DNA and use it as input in the (recently remastered) Monster Rancher games to generate a monster? Apparently those games use external user-provided data (like music CDs, game discs etc.) to generate the monsters the player would then train and use (something I only recently learned about through gaming livestreams).
I'd actually like to see the level of jank that would come out of something like that.
Also your dna is bootstraped from your mothers cells. And the prenatal environment has quite a large effect on development so your simulation might end up quite different from you if we only started with your dna.
What was unthinkable 50 years ago, playing chess better than a human, it's now trivial for a $100 device.
And it's not necessarily required that to simulate the growth of a human you'll need to simulate the entirety of chemical reactions in all 50 trillion cells and all that.
It's unlikely even if we improved computing hardware many orders of magnitude beyond all reasonable predictions, that the calculations would be able to simulate all the necessary details; most of our simulations now are based on many approximations due to hardware limitations.
As to the question of "what level of fidelity is required to turn a FASTQ of somebody's genome into an accurate model of the resulting human, with some sort of realistic environment also provided", that's so far beyond what is even remotely comprehensible it's not worth speculating about in terms of science fact; it's just fiction.
For example today we can already predict the color of the eyes and other phenotype from the DNA.
If you are able to observe enough samples of cell growth and their associated DNA, you probably can model and predict the statistics of a cell from their DNA. Because the cell is itself the result of a lot of chemical processes, the law of large number will help smooth those statistics.
Given that we have a lot of cells, the collective behavior is probably entirely governed by these statistics.
We could even do that, without knowing anything about DNA at all. Or predict tomorrows weather without satellites and computers.
I think you are a bit too enthusiastic about statistics, or too naive about complexity.