This anecdote is presented as the norm, but it’s actually far from it.
“Minimum wage” is the tip off that the journalist went out searching for the most extreme anecdote they could find. For all the talk about minimum wage jobs, only around 1% of jobs actually pay federal minimum wage. That number is falling rapidly as it becomes trivial for anyone to walk into a $15/hr job with benefits almost anywhere except the smallest towns.
Of course it’s not possible for someone earning minimum wage to save up money and buy a house in their 20s. Minimum wage jobs are literally the lowest paying jobs a person could possibly find. Anchoring expectations that no job should exist unless it pays enough to buy a house in your 20s in any city you want is blatantly unrealistic.