The quickest way to learn to speak Polish or any other language is through the total-immersion method as pursued by Berlitz and other schools using similar appoaches. It means 6-8 hours of exposure a day for a minimum of two weeks (two months is even better). There, at lunchtime you don't even get the salt unless you ask for it in Polish, and the question "Where's the nearest loo" will draw only a blank stare from teachers and management.
The downside: the cost and daily time budget which not everyone can afford.
By progressive, do you mean long and drawn out? Of course that is also possible, but not everybody ahs got tyje time and patience for that. The Berlitz method replicates the way a child learns its own language through constant exposure. Except it is more condensed because the learner knows why he's there and that it's costng him dearly.
There are all kinds of metods. Do you know of any other than total-immersion that produces quicker reuslts, for instance after 2 weeks, 2-6 months or 1 year of study?