I'm not sure about leveling the audio automatically. You could probably find an effect that does this, after all audio normalisation is a pretty common feature even in audio players, let alone editors. However, I doubt that it would give the exact result you want and given that you are using Premiere Pro, you will probably want more flexibility and manual control.
There is an easy way to do this on the go while watching the video though, which is the Audio Track Mixer. Note that using this method requires you to use one audio track per audio type (e.g. one track each for voice over, ambience and music), which is advisable anyway.
First, open the Audio Track Mixer for your sequence by selecting it in the menu under Window → Audio Track Mixer. There you will see all the tracks in your sequence, along with volume controls for every one of them and the master track (all individual audio channels are mixed down into a master track for the export, but that is another topic entirely). Now, you want to change the Automation Mode of the track with the audio you want to adjust from the default setting Read to Latch, Touch or Write. Then you can simply start playback using the contols on the bottom of the panel and use the volume controls to adjust the volume on the fly. Premiere will save the set volume levels over time.
The Automation Mode setting changes how the volume controls behave:
Off Ignores the track’s stored settings during playback. Off allows real-time use of Audio Track Mixer controls without interference from existing keyframes. However, changes to the audio track aren’t recorded in Off mode.
Read Reads the track’s keyframes and uses them to control the track during playback. If a track has no keyframes, adjusting a track option (such as volume) affects the entire track uniformly. If you adjust an option for a track that’s set to Read automation, the option returns to its former value (before the current automated changes were recorded) when you stop adjusting it. The rate of return is determined by the Automatch Time preference.
Write Records adjustments you make to any automatable track settings that aren’t set to Safe During Write, and creates corresponding track keyframes in a Timeline panel. Write mode writes automation as soon as playback starts without waiting for a setting to change. You can modify this behavior by choosing the Switch To Touch After Write command from the Audio Track Mixer menu. After playback stops or a playback loop cycle is completed, the Switch To Touch After Write command switches all Write mode tracks to Touch mode.
Latch Identical to Write, except that automation doesn’t start until you begin adjusting a property. The initial property settings are from the previous adjustment.
Touch Identical to Write, except that automation doesn’t start until you begin adjusting a property. When you stop adjusting a property, its option settings return to their previous state before the current automated changes were recorded. The rate of return is determined by the Automatch Time audio preference.
For speeches, I would recommend you use Write, Touch is better suited for music or other more dynamic audio.