As per title. Stalin invaded some 16 days after Hitler’s entry into Poland. Why did he not invade at the same time?
The Soviet Union did not want to begin a war in the west until it had security guarantees in the east. After Nazi Germany, the foremost perceived threat to the Soviet Union was Imperial Japan, which proved to be somewhat true in a series of border conflicts starting in May that culminated in the Battle of Khalkhin-Gol in that August. Just three days after the end of the battle (23 August), the Soviet Union signed the Molotov-Ribbentrop pact with Germany. However, the conflict with Japan remained unresolved for several more weeks. This left a possible threat of Japanese invasion in the east. With a ceasefire with Japan in effect on the 16th of September, Stalin felt secure in fulfilling his end of the Molotov-Ribbentrop agreement, and invaded Poland on 17 September.
Sources:
Beevor, Anthony. The Second World War. 2012, Back Bay Books.
Goldman, Stuart D. Nomonhan, 1939; The Red Army's Victory That Shaped World War II. 2012, Naval Institute Press.