An increase in recorded cases can be attributed to an increase in infection rate only when the increase is not accompanied by more testing. The US tests 1.75-2.0 million people a day. In September that number was 800,000.
To look at infection rate, what you want to look at is percentage of tests given that came back positive, and while numbers will be skewed if you're only testing people with symptoms vs people who ask vs everybody, it is good to see a high test rate and a low positive rate. 250k positive from 1.75-2 million tests is ~15% positive rate.
Also the death rate per positive test being low is a very good thing. That number, according to the CDC, is 0.6% and falling.