Einstein made many predictions, including gravitational waves and the possibility of black holes.
Relativity is taken into consideration for the Big Bang model, so did Einstein agree with it or did he have a different view?
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Einstein's opinions were not static, and he lived at a time when there were several competing theories and not much observational evidence.
Einstein introduced a cosmological constant $\Lambda$ into his equations, the purpose of which was to allow for a steady cosmos with no expansion or contraction. He is said to have later regretted this addition. He was aware of Hubble's observations of galatic redshift, and Lemaître's "hypothesis of the primaeval atom". But along with most physicists in the 1920s he did not support it. He suggested an oscillating model in the 1930s, but rejected it later (apparently because it didn't solve the problem of entropy)
His final opinion then seems to have been "we don't know". When he died in 1955 there was no consensus, and Einstein was by then an old man and not actively involved in research physics.