Sure, the ATTiny series doesn't have an onboard DAC but it has hardware PWM channels which top out at around 32kHz base frequency for an 8MHz internal oscillator clock, 8 bit for the PWM. For a max frequency output say 1/10 lower a two pole Bessel should work fine to filter that, maybe even just a buffered RC.
The internal pseudorandom modulation source for the PWM output could be
1-dimensional Perlin noise: