What can Tom do relatively quickly to show there's a change? He can start by not following the exact same strategy of making marginal additions to a deeply flawed roster in hopes it results in a legitimately competitive team, which is what they've done for the past two years. For all his talk of "we can't keep doing the same things and expect a different result," every indication based on the moves they've made thus far and what Falvey has stated the free agent budget to be is that they are, in fact, using the exact same strategy. And based on Tom's quotes and the supposed timeline of Joe getting pushed out (a month ago), this is Tom's strategy, or at least one he's agreeing to go along with.
They are not a Pete Fairbanks away from having a competitive bullpen (no one currently on the roster is worthy of a top 3 slot in a competitive bullpen - not yet, anyway). They're not signing O'Hearn (which I wouldn't hate in a vacuum) on top of Bell with the budget they have and all their other needs. They are not set up to be competitive with a $115MM payroll and the current make-up of the roster. Before someone brings up the Brewers, that roster was balanced perfectly. They were above-average in just about everything. The Twins as currently constructed are ... not.
That would leave two options - well, three options, but it's probably too late in the offseason to can Falvey at this point - to demonstrate change.
1. Crank up the investment in the roster if you insist that you can be competitive while you still have control of Lopez/Ryan. At a bare minimum, that means restoring payroll to at least the level of last year so you can demonstrate that the Correa savings actually are being reinvested into the roster. That would go a long way toward showing fans that it really was a baseball move and not a cost-cutting one. This path would be more fun, but probably not fiscally realistic at this time. Plus, the flaws in the roster might be too significant for even that level of investment to overcome, and a failure of this strategy would put them in the worst possible position when Lopez/Ryan/etc are gone. Which leaves:
2. Start the rebuild for real. Move your most valuable assets and target 2028 for real competition. Surely this would disappoint some fans, but just as many would see this as a path toward actual competitiveness; a sign that we're finally getting off the hamster wheel and making moves with an actual championship window in mind. You can still do all the fan engagement stuff you mentioned. If you're targeting kids to fill the seats (which I agree you should be), they're not going to be turned off because they won 65 games instead of 72. But they will be able to start to identify with the young players that would be the core of a team that's ready to rock in two years. Now compare that hypothetical roster - one that's been supplemented with the returns from the trades of your valuable assets, plus the truly impactful free agents they'd be able to afford - to whatever would be in place after another couple failed runs at mediocrity. The difference is night and day.
That's my realistic/pessimistic (depending on your point of view) take. If you truly believe that they can be legitimately competitive (not outside-shot-at-the-third-wild-card competitive) with this roster and budget, then I think we're in "agree to disagree" territory