Q: Started with new battery once, but then wouldn't the next day

Yesterday, I started my car, drove some distance and then the car suddenly wouldn't start for the drive home. The battery was old, it was cold out and the car started with a jump, so I figured that was the issue. Bought a new battery and installed it. Immediately afterward, it started without issue. About 4 hours later, I started it again with no issue.

This morning, however, same issue again, even with the new battery. Could start it with a jump from my charger, but not on its own.

There's no clicking or grinding, so I don't think it's the starter, and no visible corrosion on the terminal clamps, which were apparently on tight enough to give energy to the power locks and power sliding door, so that seems unlikely.

But I'm a rank amateur at all of this. Is the alternator all that's likely left?

My car has 117277 miles.
My car has an automatic transmission.