To put into perspective how improbable a finite number of monkeys can reproduce a single work of Shakespeare in a finite period of time consider this.
If we use 10^80 monkeys with typewriters ("roughly" the number of atoms in the Universe) and a typing speed of 1000 keystrokes per second for a period of 10^150 years (the time to the predicted heat death of the Universe), the probability of a single work of say Hamlet being reproduced is a 1 in a 10^183,000 chance.
Not very good odds in a BB universe.
Obviously one cannot draw direct comparisons between monkeys randomly typing on typewriters and the evolutionary chances of ET, except to say the chances for ET's existence seem intuitively far better in an infinite steady state Universe than a finite BB universe.
Regards
Steven