star - Sun from SuperNova

Actually yes, gravity is too weak to do the job by itself.
But as you mention, another force is acting on the system too, in a very strong way: it is the pressure that pushes outwards. In fact, the energy released by the explosion of the supernova, helps to compress the layers of released material (gas and clouds). You have shocks between the expelled gas (fast) and the ISM (slooow). Also, you need cold gas to produce a collapse event, and the ejected material from an explosion is not cold at all!

So, you need an efficient mechanism to induce collapse of the gas cloud, and this mechanism is furnished by compression instabilities.

You start from the Virial theorem: $2K + U = 0$

with K kinetic energy and U potential energy. What you want here, for your collapse is that the gravitational potential energy is larger than the kinetic energy (otherwise particles energy will overcome the gravity and avoid collapse - not exactly true, but you can think as if high energy particles pushes outward).

Then you can rewrite the Virial theorem as:

$$3 N K T = frac{3}{5}frac{G M^2}{R}$$

where K boltzmann constant, N atoms number, M mass of the cloud, R its size.

In our case (collapse case) the left term must be less than the right one.

Then you can transform $N = M/m$, with m mass of the single particles, and $R = frac{3 M}{4pirho}$, with $rho$ cloud density (assumed constant).

Than you can calculate the Jean mass as:

$$M_J = (frac{5KT}{Gm})^{3/2}(frac{3}{4pirho})^{1/2}$$

This is the limit after which your cloud can collapse.
Look at the dependence on the temperature, and the inverse dependence on the density.

Just to give an idea of the typical values encountered, we can still rewrite the critical mass as:

$$M_J = 2M_{sun}(frac{n}{10^5 cm^{-3}})^{-1/2}(frac{T}{10 K})^{3/2}$$

Source: this lesson

PS: a similar mechanism is triggered by the rotating arms of spiral galaxies.