Back in 2018 I did Andrew Ng's course in Machine Learning on Coursera. It was pretty much "from first principles" in that you learned a bit of linear algebra and then you implemented algorithms in Octave, working up to MNIST etc. I felt like I came out of it with a good understanding of the basics, and that ML is maths not magic.

Looks like the course has turned into a multi-course "specialization" and I have no idea if any of it is the aame as the course I did. But it might be a place to start.