When they are pups I manhandle them daily. Looking in ears, mouths, holding feet, pinching toes. It teaches them tolerance. It prepares them for a vet to examine them. It also calms down reactivity. It's why I always get pups. The more you mess with them when they are very small the better they are as adults with accepting being held and handled.
As far as teeth brushing, I grab a lip and stick the brush in and brush. It doesn't have to be for a long time as the toothpaste has an enzyme in it that helps to remove the tarter. Never had a problem. I use the angled brush. It has made it so I don't need to do dentals except for the boxer occasionally needing her gums trimmed.
I did all this, except for the mouth. Completely skipped the mouth. Surprisingly, he's OK with me touching his mouth when it's just my hand (probably because of the show training). When the toothpaste and the toothbrush comes in however, he's like "nope, I'm outa here"