I wrote a subtractive synth in java for my masters project. It was a fascinating domain to learn. For example, how to manage the independent voices, wavetable interpolation, envelopes. I was probably in over my head, and if I recall correctly, my supervisor was warning me about the complexity, since it was a software engineering programme.
The filter was the weirdest, least intuitive part. I ended up porting some open source code to java. This eventually worked, but was essentially impossible to debug without some sort of software oscilloscope.
That was about 18 years ago (yikes), and I still think about DSP from time to time.
The best intuition I have of low pass filters is to imagine it like an averaging, smoothing function which operates on the sample values as a sliding window. But that's not really true - it's not a straight rolling average, instead the sinc function (sin x / x) is used to scale the sample values with respect to time.
The way FIR filters work assumes a finite amount of samples (otherwise it would be technically impossible to know all past and future samples), so instead you pick a time period over which to calculate the output. Since there are always past and future samples included, this leads to a delayed output. Eg for a 100 sample filter window, you'd need to first have 100 samples in order to calculate the first output sample. This is intuitive, since a filter is sort of a smoothing, averaging function.