Pilot reported a CFIT event during initial departure in which the pilot deviated from the assigned heading. ATC assigned a corrected heading and flight continued safely to destination.

Narrative

Instructions on take off were fly heading 230 and climb 3000 ft.; expect 6000 ft. after 10 minutes. I purchased the aircraft in DATE; and began training in it at the end of DATE1. It had been the warmest its been since owning the airplane; and I noticed the lack in climb performance compared to previous trips. Taking off Runway XX at ZZZ; I wasn't confident I would clear the trees on the top of a hill; so I made a right hand turn to follow the river. I then contacted departure on the assigned frequency; but I forgot to correct my course back to the assigned heading after clearing the trees. My initial right turn took me close to direct to my destination as indicated by my G5; and I believe that confirmation bias gave me the sense that I was doing the right thing. Upon contact with departure; the controller quickly asked to confirm heading 230; I apologized for missing the heading and then corrected with no near miss or conflict. To prevent this from happening again; I believe a quick reference to my notes page 'CRAFT' after final call to ZZZ would have reminded me of my instructions. I had set the heading bug of the G5; but that was not a clear enough reminder. Adding the reminder to my climb-out checklist also would've prevented this from happening.