I think it's a combination of at least three things.

Cosmic Microwave Background radiation gives us a pretty good idea of the energy/mass density in the universe at a fixed point and age of the universe. If you take the densities estimated from the CMB and multiply it by the estimated size of the universe at the time the CMB (380k years after the Big Bang), then you get the total mass.

Second, we can just look for what we can see. I think there have been large-scale surveys done to estimate total mass/energy in the universe.

The third estimate has to do with something called 'critical mass' - we observe the overall 'curve' of space to be very close to flat. I'm talking the geometry of space; two parallel rays of light do not ever cross or diverge. For this to happen, there needs to be a certain average density of mass.

Wikipedia has the mass of the observable universe listed as 1.5×10^53 kg, although this can go up to 10^60 kg at the higher ends.

If we plug the Wikipedia numbers into the Schwartzchild radius formula: r = (2GM) / (c^2)

Where G is the gravitational constant, M is our mass, and c is the speed of light:

r = (2 * 6.67408 * 10^-11 m^3 kg^-1 s^-2 * 1.5*10^53 kg) / (299792458 m/s)^2

r = 2 * 10^43 m^3 s^-2 / 8.988 * 10^16 m^2/s^2

r = 2.225×10^26 meters

r = 23.52 billion light years

Wikipedia lists the radius of the observable universe as 46.5 billion light years.

So... given the Wikipedia numbers, the universe would need to be half the size it is now to be a black hole. At these scales, being within an order of magnitude is... fine.

If we bump up the estimate of mass to only 3x10^53 kg, then the Schwartzchild radius equals the size of the observable universe.

So it's within the margins of error of our current estimates that the Schwartzchild radius of our universe would be the current size of our universe.

Approximately

Light from stars tells us how big they are then adjust for things that don't emit light by looking at how objects move (i.e. gravity). Objects in this case not necessarily being single entities but often groups of things like entire galaxies. This is basically how dark matter became a thing. Scientists were like "hey theres waaaay more gravity moving things around but we dont see any objects causing it...."

It's less than time and space switch in a singularity, and more that they are "undefined".

Like dividing by zero.

It's more complicated in ways that aren't intuitive.

Yes, at first glance, it appears that everything would continue to collapse down to a singularity. But a singularity is literally a failure of our model of physics. It's like dividing by zero- the result is nonsense. It's not an actual object.

From our perspective, time is stopped at the event horizon of a black hole. The singularity never forms because there isn't time for that to happen. If you fell into a black hole, would a singularity form as you are crossing the event-horizon? Maybe. Maybe Hawking Radiation is a thing and you're cooked by a wall of radiation as the collapsing object literally evaporates beneath you.

Keep in mind that high densities are needed for stellar black holes to form. An event horizon would form around the solar system if it was filled with air- and yes, there are black holes of this size.