How to add public transit on Google maps

Honestly it is not possible, @Laurent
Timetables may change frequently, and are used by Google Maps to calculate the time of your itinerary.

It will be quite disappointing for a user to discover that a train, or a bus, is no longer available because they changed the schedule yesterday.
That’s why Google Maps gives the possibility to the travel companies to join for free the Transit program, with mutual benefits for the company (his itinerary will be made available and suggested to the users) and the users, that will have more options.
A great step could be to contact the company and to share the link, because they may not be aware of this possibility