The Ishtar gate was built in 575 BCE by king Nebuchadnezzar II.
But this is a replica. The even larger original was discovered by German archeologists in 1904. Since they were also the ones funding the excavation ⛏️, they felt entitled to smuggle most of the discovered material back to Germany.
Despite repeated requests by the Iraqi government to return the gate, you still have to go to the Pergamon Museum in Berlin if you want to see the original.