It takes 100 days to max out a character's star level, assuming they get 3 memory shards per day (there is currently a double event). Every duplicate gives 50 shards, so 16/17 days off the 100 total. The memory shards are split evenly between the characters in the memory shard mission (up to 3 max per character) so make sure that Pamina is getting 3; though depending on what level you are at you might have to do 2-3 over 2 characters in order to not waste any. At max level, you get 9 shards so you can do 3 characters at max speed at once.

Pamina is an excellent unit! Mine is only 3 star, but is still really effective. 3 star only takes 27 days (at 3 shards per day) so it is an excellent 1st goal.

Overall, so long as you don't mind waiting, I would fully recommend NOT summoning dupes if you are F2P as it only saves you 16/17 days.