How to produce uniformly distributed low-frequency noise?
Well, this is one way you could do it: with LTspice, use the white() function. There are also rand() ([0,1] V, pulses) and random() ([0,1] V, smooth pulses), but white(2*fs*time) will give you what you want between [-0.5, 0.5] V:

B1 is a behavioural current source (bi, or bi2, as it appears in the component selection dialog, F2), and the .wavecommand exports it as a .wav file named output.wav, with 16 bits resolution (can be anything from 1 to 32) and 44.1 kHz sampling frequency (can be any number from 1 to 4294967295). For this case, the file is 8,820,046 bytes, which can be imported. This is a 2 Hz white noise, band limited, properly sampled signal, 100 sec long. Optional settings can include a tighter timestep, though opt plotwinsize=0, here, disables waveform compression and for a 2 Hz signal, it may not make much sense.