Is it possible to do ADC SCAN conversions without using DMA?
No. And it is not practical.
For individual samples, there is Injected mode.
For multiple you can trigger the ADC to load a small array quickly, and where you would have waited for EOC you wait for DMA TC.
Where samples are occurring on a timely basis, use a TIM to trigger the start of conversion, and then manage in the IRQ Handler.
Best to move beyond the polled mentality.
Retrieving data ...