Maybe 3 might be stretching it, but for me there's quite a lot of work to do for the reasons you've given.
We need to retain our best players, this becomes more difficult the better we play and more success we have (see Tav last year).
We're also pretty reliant on loans too. Fine if that's the model but it does mean that each summer you're either a) looking to sign those players permanently (expensive), b) extending loans or c) finding more loans signings who will fit and won't detract from the overall quality of the team.
Finally, the squad is currently imbalanced in my view and we need more depth. Our medical setup has improved (evidenced in fewer injuries) but they will still happen and we're short on options in key areas of the field - central mid and the three behind the striker for starters.
Even just looking at the loans for next season, think City are unlikely to sell Steffen and Archer and Giles are probably 12-15mil combined.
I don't think a three year planning cycle for automatic is unrealistic (calling this season year 1).
Expanding on the points I've made certainly indicates that, but this year we'd have been in with a good shout to justifiably target the autos had the season began when Carrick took over or had he been here from the outset.
Other than the sides coming down with parachute payments (Watfords, Burnleys, Norwiches) that obviously have a head start, that's the way the majority of the other sides "make it", find a manager who just fits them with the squad they already have available, add just a few key additions and throw a smattering of luck into the mix. They then go up the season it happens or the next at the most. (Huddersfield, Brighton, Forest)
There are sides that "build" for more than 2 seasons such as Brentford (I wouldn't include Bielsa-led Leeds in that bracket as they had got minted, which put them into the same bracket as the parachute possee,) but in the majority of non-parachute promoted sides they tend to make it in one season or two seasons at most from the start of their transformation.
I'm always wary of compiling tables based on a subset of data as results can be skewed a tad, but giving Carrick the Preston game (where he was basically a spectator, making observations and plans based on what he saw, but couldn't have much in the way of input that affected the game as he didn't know the side) as his only pre-season and his only squad additions to make it his being Archer on loan and Barlaser who hasn't touched a ball yet, here's the table of the Championship from after his "Pre-Season" to show how success can be a lot more rapid than season after season of careful planning;
Team Played Points GD GF (Where tied)
Burnley/10. 28. +13
BORO/12. 28. +12 (24)
Sheff Utd/ 11. 28. +12 (20)
West Brom/11. 27. +12.
Sunderland/11. 20. +8
Coventry/13. 19. +3
Watford/12. 18. -1
Hull/12. 17. +6
Luton/10. 17. +4
Millwall/10. 16. +4
Preston/10. 15. -3
Norwich/10. 14. +3
Aside from the obvious "relative surprises" such as Norwich being sat all the way down in 12th, Hull in 8th and Blackburn failing to get a mention in the top half at all, some other things are clear.
Whilst two thirds of the sides have a game or two in hand on us, the autos (and title even) look like they're essentially squaring up to be a four horse race, packed tight as sardines whilst the rabble up the road head up a more spread out set of teams some distance behind.
Had Carrick's arrival (and performance thus far being equal) been at the start of the season then even if he hadn't had the summer transfer window the data points to his effect being astronomical in terms of the "manager fitting a club" with us perceivably battling for the title despite bringing in only 1 player of his own for the last few weeks that has had time to play any minutes whatsoever.