Air carrier First Officer reported ATC gave the flight vectors for the approach that placed them below a segment altitude and resulted in an aircraft terrain warning due to a nearby tower.

Narrative

Conditions were IMC; light turbulence with some bordering on moderate; and we had been navigating around cells. We were at 3000 ft on a perpendicular heading to the final approach course. ATC said 'right turn 030 maintain 2500 till established cleared ILS 6L'. I read back the clearance and the captain selected the altitude; VS down; then selected the heading. As the airplane began to turn to the selected heading the Captain selected approach mode and LOC was immediately 'captured'. The airplane stopped turning when LOC was captured and continued on a roughly perpendicular heading towards the final approach course. After a few seconds of this we realized the AP was going to blow through final so the captain disconnected the AP the began a RH turn. I keyed the mic and informed ATC of this then looked at my PFD which showed us 2500 ft and 1/8-1/4 scale left of final approach course and in a right turn to correct the CDI. ATC said 'right turn 090 to rejoin still cleared ILS 6L' I glanced down at my panel for my RT switch (lower pedestal) to reply and heard 'bank angle'. I immediately looked up and saw ~35* of bank and 2450 ft altitude the captain quickly corrected. I repeated the clearance to ATC and then we got 'terrain terrain' we quickly executed an escape maneuver; then got vectors to come back and re shoot the ILS. We properly reported the GPWS to ATC; and the go around/APR use to Maintenance and dispatch. I didn't think too much about being given 2500 ft as ATC commonly has minimum vectoring altitudes lower then published altitudes however in this case the lowest altitude on this segment of the approach plate was 2700 ft and there was a tower that is 1529 ft tall just left of the final approach course. With us being at 2500 we were only 971ft above the tower and I believe this was likely our cause for the GPWS.