I guess the story that T-34 design given to the USSR lend lease was an urban legend.
The Russians had some excellent engineers. A lot of times they had to work around the political commisars, but the press of war got things done.
Yes. Design of what would become the T-34 started in 1937. First vehicle production commenced in 1940. Lend Lease to the Soviets didn’t start until mid 1941.