Academic performance in a math class with a low average

[mvpfam]

For context, I am a freshman at a pretty highly ranked university for math (around T20 in NA) and I intend on pursuing Math and Physics as an undergrad, and hopefully a PhD in Math. In my first semester, I have to take a course on Algebra and Analysis as a requirement. Although I have been performing decently well (probably A- / 3.7 out of 4.0 ), the class average for both course has been around a C (2.0 out of 4.0). Moreover, after looking at multiple blogs/forums/videos about Math PhD apps, I feel disheartened for getting around a 3.7/4.0 when many people (not everyone) in other universities obtain close to a 4.0. Moreover, my university awards a High Distinction (the highest honor possible) to those who graduate with a > 3.5 GPA (around 20% of the graduates obtain this honor). So, if I possibly end up with a 3.7 GPA and get a High Distinction, will the grad school committee (mainly in top US universities) care about my performance relative to the graduation class? Or, will getting a 3.7 make it even more difficult for me to get into a top school? (I am cognizant of the fact that research/good recommendations matter a lot as well. I am just concerned about the transcript/grade side of my future application.)