Has anyone ever attempted to make transient spice simulations including noise? If so, I would be very grateful for some exchange!

Yes, and it's a bit tricky.

What about using Transient noise source or Random voltage source provided by ngspice ?

In ngspice, something like this:

.control
noise V(VBGP) VVDDA oct 10 ${FREQUENCY:SWEEPSTART} ${FREQUENCY:SWEEPEND} 1
let vn = sqrt(onoise_total)
echo ${FILENAME} $&vn
quit
.endc

This is a snippet from noise analysis on a bandgap. The file is a template and the

${...}

entries are variables that get substituted by a script before the netlist is passed to ngspice for simulation. The purpose is to get a single value for RMS noise related to the power supply in the given frequency band.

@Krzysztof Herman I would like to use the true parameter of the BSIM model

@Lukas Bongartz I got your point. My first guess was that you want to observe your system/circuit response to the noise applied to the input

The small signal noise sources in the SPICE models (including BSIM) are not necessarily suitable for transient noise because they're only characterized up to PSD (and as far as I'm aware, simulators don't even try). You could turn them into transient sources by assuming gaussianity, but it's not clear that you'd get sensible answers out, because the PDKs weren't designed with that assumption in mind necessarily. Also, the way that ngspice does transient noise is a bit weird, and there's some question of whether it's mathematically sound.

It is possible (and useful) to do transient noise simulation from device models using commercial simulators like Spectre. It is not possible in any open-source simulator, it's a big missing gap in opensource capability.