The modification is usually done at some point close to the time of conception. Since it is the DNA of the entire organism, the founder, that is changed, it can pass the transgenic gene to its offspring. Another term sometimes used when speaking of transgenic organisms is chimera.
Chimeras result from an embryo that is a mosaic of original cells and engineered cells.
The first transgenic organism was produced in 1975 by Jaenisch and Mintl. The organism was a mouse with an ape transgene. The protein was expressed, but was not passed on to the offspring. The same group produced the first strain of transgenic mice in 1977. In 1974 the first chimera was produced by R.L. Brinster.