It takes 3 years on average of doing all 70 monthly challenges every month to get ONE desired champion to 5 stars. Math inside. This is essentially unattainable to f2p players.

Monthly challenges are the only renewable source of star crystals, you get 1 silver vessel and 1 gold vessel per month.

Silver vessels give 5 star crystals, gold give 10. But they are from a random region, meaning there is a 1 in 11 chance you get the region you want.

So the average amount of star crystals you get of your desired region per month is 15/ 11= 1.36 per month

It takes 50 star crystals to get to 5 stars. 50 / 1.36 = 36.76 months = 3 years average.

Adventures will give you some Vessels for a 1-time reward. According to the wiki, doing all adventures gets you 12 silver vessels and 6 gold ones. So that does bump you forward about 8 months, so about 2 years and 4 months to get your first desired champion to 5 star.

Keep in mind, this is random. If you have good luck, it can be faster, if you have bad luck, slower.

I didn't even bother to do the math on 6 stars because with how bad 5 stars is, I don't even want to think about 6 stars. In reality, 4 stars is really the highest f2p players will be able to achieve before the grind gets too insane, assuming nothing changes. Riot really does need to add more sources of Star vessels. The 1-time adventure rewards are nice, but it is not a long term solution.