B737 First Officer reported a wrong heading input that was not caught during cross-check led to disorientation and unintended turns during a departure in moderate rain and night conditions. Time constraints and mismanagement of the autopilot during high workload also contributed to the error.

Narrative

We were taking off out of ZZZZ in moderate rain; and in the middle of the night. A few hundred feet after takeoff we were in IMC conditions. At 400 ft.; the aircraft commanded a turn I was not expecting. Once the incident was over; we realized that we had the wrong heading in the heading select; which caused a 180-degree turn to the right when reaching 400 ft. When the Captain realized the unintended turn; they continued the turn to the right to stay clear of terrain. They became disoriented and asked for a heading that was not going towards our course. They then asked to be put into LNAV without putting our second fix at the top of the legs page; so they created another 360-degree turn to try to fly to our first point over the airfield. I missed this mistake in my cross-check.After they recognized this mistake; they asked to be put back in heading mode and while doing so they banked the aircraft to 45 degrees. I pointed out the error and helped the Captain get oriented again. We continued our climb and got on course while staying away from terrain during this entire event. We also always maintained an appropriate airspeed the entire time. As we debriefed this event when we reached cruise; the Captain felt that this happened due to rushing to take off before our clearance void time; which caused us to miss the error of having the wrong heading in heading select. They also felt that it was caused by not properly using the autopilot during a high workload environment. Also; of course; taking off at XA00 in the dark; in a rain storm; [and] without ATC present added an additional level of difficulty.