They don't have to get out of the bottom three - they just have to improve from here on out.
Up until a few games ago, the Brewers were in first place, having just dominated the second place team yet again. 11 games over .500 and in first place despite having terrible hitting. Now they've (presumably) upgraded extremely weak spots in the lineup without giving up much of anything.
With the pitching and fielding the Brewers have, even just "ok" hitting gives them a chance. Do I think they've closed the gap on the Braves? Of course not. But they weren't going to, even with a blockbuster trade, and at least as it stands now, they still have all the young guys that we hope will be the stars of the future.
If the trades work as intended (and obviously, who knows - see 2022), the Brewers will absolutely have a shot to make a run in the playoffs if they get there. Outstanding pitching and fielding with improved, even if still below average hitting, won't make the Brewers World Series favorites, but will give them a shot to beat anyone in a series.
I just don't see the point in emptying the farm for, say, Soto, when you can keep all your prospects and not be much worse off in the present.