Therefore, do you think that a source of income must be steady enough for years, before one can be financially free or rich or very wealthy, depending on the source(s) of income?
It depends on what the source of income is, if the source of income is your salary, then "steady" would mostly mean monthly, though it is difficult to become rich or wealthy with just a salary. If you are investing in something like BTC or real estate, you cannot really call your income "steady", but your investment can be up 30% in your sleep, and for me that is how people become financially free in the long run.