Like all big cities in China, it's a real effort to get out of town. The standard is to take a cheap bus to a small city then continue hitchhiking.
In October 2019 Worldhitchhiker hitched out of Chongqing to Leshan, this spot is also suitable for Chengdu. Take public transport from the Chongqing to a bus station near G85 Jiulongpo Toll Station, it took me some effort from Chongqing downtown (Jiefangbei district): 1 metro ride, 2 busses and a 40 minute walk to get there. I used A-Map app to find this connection (how A-Map works and helped hitchhiking in China), use it to find the best suitable public transport connection for you. The toll booth is huge and outside of the metropole Chongqing, there is some place to stop cars. Unfortunately the police sent me away after 20 minutes hitching behind the toll booth, so I walked in front of the toll booth. From there it took me another half an hour to get a car in the direction of Leshan.