The OP states a "Mosquito-like bomber", no the Mosquito itself...
...that is built either from aluminium or wood.
It is good if they can use Packard Merlin, but V-1710 will do.
They can build, say, a wooden transport aircraft.
The OP states US as a producer, and the USA was in position to build a V-12 powered bomber already in 1940, if they founded they need one.
What does Mosquito like actually mean? How similar does it have to be to be Mosquito like.
Why I thought the year was important is teh Mosquito's first light was in November 1940, introduction 1941, and didn't get into wide spread service until 1942.
We could argue that several twin engined aircraft were Mosquito like but were simply not able to do some jobs as well as a Mosquito. I would think if we wanted to match the Mosquito then we want a Mosquito. I would argue use the mosquito until something better can be found or until the need no longer exists.
By the time some saw the merits of the Mosquito a lot of other planes were already being built and were already in existence.