The “new” alternator could also be bad. Measure the volts on the battery terminals while the engine is idling. You have to get close to 15V. Otherwise the battery is not charging.
If you only replaced the alternator regulator then probably the alternator needs new brushes.
Other possible causes: bad ground connection. Check the battery negative wire where it connects to the chassis, also, the engine’s connection to the chassis, corroded battery terminals.
Maybe the battery is damaged internally and does not hold any charge. It sure sounds like that.
Also look for shorts that could drain the battery fast and kill the regulator.