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.