Does the expression of amplitude modulated suppressed carrier even exist in reality?
Negative frequencies exist (outside of complex math) in strictly real signals only in relation to a higher frequency carrier frequency, and only over a long enough observation window to discriminate them orthogonally from the carrier and any other sidebands.  (Over shorter time windows, spectral content is very likely ambiguous.)

Negative frequencies can also exist at baseband as complex IQ signals inside an SDR algorithm (FFTs, et.al.).  Negative frequency signals have the opposite relationship between the cosine and sine basis vectors from positive frequency signals, and thus appear in the opposite half of a complex FFT result, which can allow an SDR radio to separate the upper and lower sidebands during USB or LSB SSB filtering or demodulation.

Essentially, quadrature or complex heterodyning allows moving a strictly real RF signal containing low, middle, and high frequency spectrum, down to baseband as mathematical complex or IQ representation containing negative, DC (0 Hz), and positive frequency spectrum, respectively.  Why do this?  At baseband an SDR radio can potentially use a much lower sample rate, and thus run on a less expensive CPU or DSP chip, and/or require less power to process (filter, demodulate, etc.)