Wikipedia covers this sufficiently at
https://en.wikipedia.org/wiki/Cosmological_constant#Sequence...The five-line tl;dr: non-expanding cosmologies with no big bang but lots of galaxies tend to collapse in finite time. One can avoid collapse with a positive cosmological constant. That approach predated the work of Hubble (expansion) and Lemaître (big bang). Expanding cosmologies with a sufficiently large initial big bang do not need a cosmological constant to keep expanding forever. Einstein, not being stupid, recognized that and carried on.
Since 1998: an accelerating expanding universe is inconsistent with just a single big bang as impulse, but is consistent with a small positive cosmological constant.
Einstein and Schrödinger certainly discussed whether to treat the cosmological constant as an energy entering into the right hand side of the Einstein Field Equations instead of a multiplier on the metric in the left hand side: [Harvey 2012] https://arxiv.org/abs/1211.6338 Their conclusion is that choice of side is principally a matter of aesthetics, and that remains true today.
Harvey2012 §5 is a good reminder not to put too much weight into the early days of general relativity. Exact solutions were few and simple but still extraordinarily hard to work with by hand. Numerical approaches didn't exist, nor did formalisms that provide post-Newtonian approximations that are more tractable. Realistic distributions of matter were largely as-yet undiscovered (compare 1917 introduction of cosmological constant and low estimates of the number of spiral galaxies in the sky, their mass, and the light-travel distance to them: https://en.wikipedia.org/wiki/Great_Debate_(astronomy) which came later).
Einstein's adaptation to the flood of astronomical discoveries during his productive lifetime is part of what made him Einstein rather than any less celebrated figure.