I am always really surprised when a coffee gets much better after letting it rest a few days or so it seems.
It's the funny thing with coffee that different beans are going to be afflicted different with the off gassing process than others. I have found that if there is a specific coffee that I am getting consistent under extracted notes from when I first started brewing it and it is fresh that if I can give a few more days it will normally come around.
The good and the bad with fresh roasted coffee is that it's giving off CO2, this gas normally protects it from staling if the beans are kept in a package because it pushed the oxygen out. And if I can assume or guess a little here I think in brewing it can at times get in the way of the water mixing with solids that come out of the coffee. So when brewing a normal brew time is not going to be able to get all the solids out that you would normally be able to.
With really fresh coffee that you get, I like to start off using something other than an auto-drip machine or an espresso maker. The reason is in those machines you cannot control for off gassing nearly as much as in manual machines. Basically you are just stuck with the time limited of the machine.
What I like to do is use a manual method such as a press or drip cone or something. The reason is that in those forms of brewing you can pour enough water over the grounds to wet them and at this time you allow the gas to come off the grounds. At this time when you pour just enough water over them to wet the grounds you should wait under there are no more bubbles coming off the grounds, this normally takes thirty to forty five seconds. This is especially critical in a pour over cone like a Hario V60 or Mellita.
Overall, a manual method is great for use with fresh coffee if you can't get good result from an automated method!