A random letter generator would be expected to hit one of the keys on the top row, a numeral, at some point in the more than 600 consecutive key strikes needed to produce the sonnet. You could not expect a random letter generator to completely avoid 25% of the keyboard for more than 600 consecutive key strikes.
That would make it non-random.
It is impossible to produce a Shakespearean sonnet at random even in infinite time.
No it would be produced infinite times.
I don't think you understand what the words random and infinite mean.
I suggest a basic primer on probability too.
Facts don't lie or have an agenda. Facts are just facts
"God did it" is not an argument. It is an excuse for intellectual laziness.