Synthesizing the DNA itself is not the only problem however.
You then have to get that DNA into a working living form state so that normal cell processes can continue:
- for viri see: synthetic virus
- for bacteria, you have to inject it into a cell
- for placental animals, you also have to somehow simulate a compatible placenta. It is likely easier for eggs.
Multicellular questions:
Apparently achieved for the first time in 2021: https://www.jcvi.org/research/first-self-replicating-synthetic-bacterial-cell by the J. Craig Venter Institute.