I think it's important to highlight that the original quote is blatantly wrong.
But Einstein's fudge factor didn't fudge for long. In 1919, British cosmologist Arthur Eddington conducted an experiment during a solar eclipse which confirmed that General Relativity was indeed true- the universe wasn't static but had a beginning.
Eddington's solar eclipse experiment had nothing to do with cosmological constants and static universes. It was a test of Relativity's predictions regarding the amount gravity would bend light. Eddington's experiment was consistant with General Relativity exactly as Einstein had chosen to describe it -- ie: static.
Friedman published, in 1922, a solution to Einstein's field equations in which the universe was not static. (I don't know why expansion is favoured in the wiki article). But here's the important thing: Eddington's solar eclipse experiment is also consitent with that solution to the field equations.
There are many solutions to Einstein's field equations.
Godel came up with one which included a particular method of time travel. But his solution required the universe to be spinning and
isn't consistent with expansion.
The calculations Einstein did, referred to by DOC's source, are like solving the differential equation:
dy/dx = 2x
Only much harder!
There are many possible solutions. Which one you pick depends on choices other than pure maths. To rule out all but one answer, you need boundary conditions, often expressed as initial conditions.
Eddington wasn't satisfied that these boundary conditions can be understood to the extent of explaining all the structure in the universe today. Some scientists of his time were. He didn't like the "loophole" they used. (His word).
The reason people have abandoned the static universe solutions to the EFEs is because Hubble showed the universe was expanding in 1929.
After that, steady state theory was still popular. It was only blown out of the water when the microwave background radiation was discovered. Eddington was dead by then. To criticise him without understanding that would be a bit unfair.
btw,
Eddington believed in God, as evidenced by the title of one of his books: "Why I Believe in God: Science and Religion, as a Scientist Sees It"