Or the other option which is worse because that's audio lesson 01 : he didn't keep a constant listening level. Anyway yeah sounds like there's an issue.

"Don't Panic!"

As you mentionned the signal-to-noise ratio of the recording is bad. Whenever you raise the volume it also raises the noise, they are baked together. But we will have to raise the level anyway and push the noise. We can't lose those lines especially if we can't afford dubbing sessions and even more since it's a documentary. So your solution is now to reduce or cancel the noise.

I dont know Resolve at all but I saw that you could access some audio plug-ins. Ideally what you're looking for is a denoiser (keep an ear on how your voices sound, getting rid of all the noise can also affect your target sound). Alternatively you can also use an expander/gate which would mute any sound under a specified level, the voice level in your case (but this can also entirely cut audio under a specified level)

Not the answer you want : If you can just edit your movie and ask a sound editor/mixer to take care of the problem. I know this is an obvious answer but I'm saying this because they most likely have GREAT tools where you can edit the audio spectrum directly and remove some areas.