when do you initiate the topic of promotion after joining a new company?

You can ask about the process on joining, if it isn’t covered in the onboarding. Most companies would be a minimum six months to a year, depending upon role and your ability ties.

Ask your manager what you should do to get the next level

Additionally you want to know what criteria you need to hit in order to even start that topic. If you are concerned about asking out right start the discussion by outlining your goals and objectives and will these meet the criteria to get promoted.

1 year in, or whenever performance reviews happen