The gain is WAY too high (although you can knock it down with the pot). Any noise will be over-amplified too. The song shouldn't be faint...
You're getting 3.3V out of the microcontroller and about 5V out of the audio amplifier so you need a gain of less than 2. You DO need current/power gain... The microcontroller can't directly drive an 8-Ohm speaker. But, you don't need much voltage gain.
If you have some powered computer speakers, try those instead of the LM386 and speaker. That will also help to isolate the problem.
Similarly, you can test the LM386 & speaker by connecting it to your computer or phone (or CD player or TV, etc.). But, the gain is STILL too high!