That's exactly what the Astros did. I had a lengthy post about the Astros payroll the last 10 years. in 2016, they were last, 2017 when their postseason run started, they were 18th. After that, they have been as high as 3rd and as low as 11th and never below league average. Made the post season every time. It's interesting how well they kept their farm system stocked with the right guys to plug in (P, SS, CF) when needed.
The Astros are a good comp to the Cubs since Houston city is going to pass Chicago as the 3rd largest city in the US in the not-too-distant future.