This is actually the single most determining factor for a good coffee.
The aroma and flavor of coffee degrades rapidly after roasting, whether you grind it or not. Grinding it accelerates the process, but you can easily get coffee in unground form, and the difference between ground and unground is visually obviously: a vendor can't sneak you ground coffee if you want unground.
How long ago beans were roasted isn't visually obvious.
In short: quality in, quality out. Any discrepancy of the above will lead to a sub-par result.
Even when buying whole beans though it only lasts a week max before I can start to taste a big difference. You can usually tell as gasses are no longer released when pouring hot water over the freshly ground beans.
Ideally you want coffee to have been roasted no more than about three weeks ago.
If you don't notice the coffee get less flavourful over the course of a couple of weeks, and then tastier when you open a new bag, then there's a reasonable chance you won't notice a sufficient difference in freshly ground coffee.
One thing you unequivocally get each morning is the smell of freshly ground coffee. It's possible this is what makes me believe I taste more flavour; either way, it's enjoyable.