I have been on two inaugural routes both entirely by coincidence.
Sometime in 1987 (I think) the (Second) Manx Air were upgrading from the Viscount to the BAe 146. I visited the IOM for 25+ years as my mother and her husband retired there. I had chosen a Friday lunch time as the cost was lower. Turned out to be the first day of their G-OJET (if I recall correctly) and the big launch was the evening rotation. All the crew were happy to say goodbye to the Viscount and there was Champagne for all. I liked the 146 (and later versions) a lot and sad to see that it did not work out, for all the reasons we know.
In December 2001, I travelled LHR-MUC-JNB (return) and learnt at the terminal that this was Lufthansa's inaugural rotation on the route, also A340 as above. There was no cake but, in the terminal during boarding the
PR department had a troop of African drummers and musicians. Unfortunately, the troop were from North East Africa ...!! Still, it gave them some money.