The president has no explicit power to go to war without Congressional approval. Certainly it’s been done, and they’ve gotten away with it to one degree or another, but they have no actual authority to do that.
The War Powers Resolution of 1973 (also known as the War Powers Act) “is a congressional resolution designed to limit the U.S. president’s ability to initiate or escalate military actions abroad.” As part of our system of governmental “checks and balances,” the law aims to check the executive branch’s power when committing U.S. military forces to an armed conflict without the consent of the U.S. Congress. It stipulates the president must notify Congress within 48 hours of military action and prohibits armed forces from remaining for more than 60 days.
So yeah.. he can for up to 60 days.