A Fast Track promotion at 4.00 doesn't dump you at the bottom of the next class. It lands you partway up it, often somewhere around the mid 3s, with a buffer underneath you. That buffer is the opportunity.
From there, a clean race or two can push you back to 4.00 and promote you again, quickly. A high-corner track and a tidy run is all it takes. People call it a double promotion, and it is completely legitimate. iRacing is just doing its job, moving a safe driver up fast.
Time trials count toward your Minimum Participation Requirement, so if you only need the participation box ticked, a few quiet time trial laps will do it without the chaos of a race.
One honest warning, and it is the same one I give in the video. What goes up fast can come down fast. Don't double-promote yourself into cars you aren't ready for. Use the buffer to race a class you enjoy with breathing room, not to throw yourself in over your head.