Not really a "nomination process", nor do you "meet" the TRB. Typically, when it's your turn, it's your turn.
TRBs happen about once a month in the squadron, chaired by the DO, and any available instructor attends. There, they review pilots in the hopper for upgrade and examine prerequisites (GRACC, coloring book, hours, etc.) and then they basically ask for any feedback (positive or negative) suggesting they should accelerate or slow-roll said individual. Nothing incredibly formal behind it.
There is a "certification board" that happens after your aircraft commander upgrade chaired by the squadron commander and usually attended by the DO and representatives from stan/eval, training, and safety. It's a 10-min meeting where they basically remind you of your responsibility, trust placed in you as an AC, and current squadron philosophies (i.e., "first phone call home wins" and all of that other risk-averse stuff these days). After that, the squadron Letter of Xs (certification tracker) is updated and you're on your way doing the Lord's work.