Far and away the most entertaining path. Who gets to carry the trillion dollar coin from the mint to the treasury? How many heist plots will be foiled? How many movies about said heist plots will be made? Will there be a elaborate motorcade that's ultimately a ruse while the coin is sent by USPS in a plain envelope?
These are bandaids. Very soon it will become apparent that the US needs to take extraordinary measures to solve its debt problem, and such measures need an extraordinary excuse, more extraordinary than the recent pandemic.
(1) discharge petition - bill from committee to a vote.
(2) Fourteenth Amendment Constitution prevents willful default until SCOTUS says otherwise. Just keep issuing debt.
(3) High coupon and low principal. 10-year bond with $1 in principal and annual $100 coupon will increase debt ceiling almost 1000X.
(4) high denominations coin minting