Intensity of the acoustic waves coming out of the speakers at the very beginnig of their “journey”

According to the formula, the intensity of acoustic waves at any given point is: $$I(R) = \frac{P}{4\pi(R)^2}$$ where P is the power of the source and R is the radius of the force (Assuming that the surface of an acostic wave is a sphere)

What, then, is the initial intensity of the wave, as it is just being generated? Is it: $$I_o = \lim_{R\to0}{\frac{P}{4\pi R^2}= \infty}$$

If the source were truly point-like, yes. But nothing is truly point-like, so no: your formula for $I(r)$ is modified for short distances (where the inner structure of the source becomes relevant). This means that, if your source is a set of speakers, then $I(r)\propto R^{-2}$ is only valid for $R\gg\ell$, where $\ell$ is, say, the radius of the diaphragm of the speaker.