As usual, the answer is "it depends what you mean". There is a large existing field (prenatal genetic diagnostic testing) which trying to diagnose genetic diseases in fetuses using different technologies. These technologies are described more in points 2 and 3 below, whereas point 1 is a somewhat academic statement about the technical capabilities of genomic technology in pure research settings which are currently not really relevant for medical applications.
I can think of 3 different answers to the question as originally posed:
With currently available sequencing technology you can never know
the full genome sequence of a human well enough to see all the potentially damaging variants. The "finished" human reference genome in
fact has gaps and errors that are constantly being corrected. For
more information about what "finished" means, see here. Only one assembly of a telomere-to-telomere human chromosome exists as far as I know, and that's only the X chromosome. Even accepting that this best available technology is good enough, it also relies on things like the ability to isolate lots of high-molecular-weight DNA, which makes it very tough to do on the amount of cells you could get from a newborn without highly invasive procedures such as e.g. sampling fetal tissue in vivo. My guess is that even amniocentesis would be very hard to get good HMW DNA from.
With currently available sequencing technology you can however test
very early provided you used IVF, at least as early as the 100-cell stage
(probably earlier). This is a chancier method that will miss a lot
of information but gives you good enough info to diagnose
aneuploidies or other very obvious variants.
Alternately, you can screen cell-free fetal DNA as early as 7
weeks (or possibly earlier). However this does not involve
isolating cells so it is potentially not what you are thinking
about. It is somewhat better information than preimplantation
screening, but rather worse information than you can get from whole
Likely none of those are exactly the answer you want, but it's also a less simple question than it appears at first: a) getting cells is hard and probably not necessary for the current tech, and b) the tech isn't actually as good as generally advertised.