I suppose it depends on the GM and what sort of adventures and opponents he has in mind. Interestlying, 3-5 advanced sounds to be just about rthe difference between a starting character in CODA and ICON. That is the older system made the Starfleet characters more skilled than the average folk.
IMO, I think that "beginning" Starfleet character in CODA are pretty much right out of the Academy, and that a "seasoned" character would probably have served a few tours or duty and something like an advancement every two years or so.
If most Starfleet Captains (at least the humans) are around 40-50 years old (at least on the big ships) that would sort of suggest about 10 advancements for a starship Captain. That7s just a "rough guideline" though. Still, I7d like to think those sensior officers learned something since they left Starfleet Academy.
I started my players off as new Ensigns, straight out of the academy with no advancements. Actually, come to think of it, the first time we played was their graduation and their assignment to the starship.
I haven't had an issue with the characters being too weak. Actually, they are pretty effective from the beginning. My concern was that the characters would become too strong too soon, given the generous advancement system. My players can advance their characters about every 3 time we play, given the game sessions were productive.
Of course, if your players have characters that have been established in their careers already, then the game has a system for that. It scales based on how much action they have seen in their duty assignments. I do not have my book in front of me, but I think it is 1 adv per year, then adjusts to an advancement for every few months of wartime starship duty. It really depends on your campaign and how seasoned you want your characters to be.
Again, during gameplay the advancements come much more quickly than you realize. I would suggest being careful not to give too much at the beginning, because customization during gameplay advancement is much of the fun for the players.
If I recall, as my books are at home, in the NG, Harry Kim was written up with 8 advancements. I'm not sure if that represents him 'newly assigned to Voyager', but i think it would, considering that even under restrictive advancement rules, he would have a good dozen or so (if not more) advancements by Season 7 end.
Though the writeups for the various Captains seem a bit light.