Apart from the population provided by the military and the necessary logistical and administrative personnel they would do it by offering free housing in an attractive location. Konigsberg is an old city by the sea in temperate climate and located closely to other countries and newly annexed Baltic countries.

Russia was undergoing a very intensive industrialization period on the 20s and 30s but being a centrally-planned economy built on the foundations of very primitive economy of Tsarist Russia they couldn't handle the massive expansion of arms industry and related heavy industries as well as providing necessary amount and quality of housing. The resulting housing shortages are troubling all of the former communist countries even today because housing takes time to build and consumes a lot of productive capacity that is being diverted away from strategic projects.

You have to remember that the population of Kaliningrad Oblast is currently below one million. That is nothing in a country of 130+ million (USSR after WW2) or 270 million (USSR shortly before its collapse).