Unfortunately Im new to Trailblazers.Mostly into Mustangs for the largest part of my life
up til a year ago when I bought an 05 model.
However,on most vehicles,when the gas pump nozzle shuts off almost immediately after you pull/lock the trigger,its usually a sign theres a restriction or leak in the EVAP system,which includes components like the gas cap,vent valve,carbon canister,purge valve and various vacuum hoses inline with the fuel tank and the engine.
However I did locate a thread on this site that listed another possible cause and the fix.
Replace the fuel tank filler upper pipe assembly and the lower hose assembly.
However,before you go out and start buying parts,scan for codes or if you don't own a scanner yourself,swing by Autozone and get them to do it for free because a code may indicate an EVAP system component is to blame instead.The EVAP system purges fuel vapors into the engine to be burned and its part of the emissions system.I know on my Mustang,the gas cap had a pressure relief & vacuum valve built into the gas cap.The vacuum valve was used to draw in air that would fill the empty space above the fuel level as the fuel level dropped.The pressure relief valve was used as a backup pressure relief valve in the event the normal venting system was overcome by excess generation of internal pressure or restriction.If the pressure/
vacuum valve is damaged/contaminated, deformation of the fuel tank could occur.Im
unsure if the Trailblazer gas cap works like this or not??
The following thread talks about the upper pipe assembly and hose replacement.