great post, welcome!
For perspective, the 2021 Twins started 5-2 as well. Then, their offense went quiet, they went into a slide, had a series cancelled due to Covid (and it was considered good timing with how poorly they were doing), and then they had that signature loss in Oakland in extra innings, and getting back above .500 seemed unlikely. By Memorial Day they were pretty much out of it.
In 2022, the Twins started 4-8, then went on a nice win streak at the end of April and built up a nice record playing bad teams in May. They battled ok the rest of the summer (fans will remember the Emilio Pagan meltdowns in Cleveland) but by September, they were out of steam.
So for 2023, I don't think we've really seen anything yet to change anyone's mind. The starting pitching has been great, but will come back to earth. The bullpen should be ok, but they will need to identify the live arms and not pigeonhole relievers into roles. Yes, managers can affect the outcomes of games. Guys like Nick Gordon and Donovan Solano, nothing personal, wouldn't be getting this much playing time for any other team with postseason hopes. They play in the worst division in baseball, but that doesn't matter if they make the postseason, when everyone starts 0-0 at that point.