Help needed with commas in a sentence

Solution 1:

If you follow the convention that is commoner in American English, which I suggest you do, defining clauses are linked by the relative pronoun “that”, which is never preceded by a comma, and descriptive clauses are linked by the relative pronouns “which” and “who”; “which” and “who” are always preceded by a comma and their clauses end with a comma (or full stop.)

All the subordinate clauses in the example are defining clauses, thus “that” is used throughout and there are no commas:

{It was the invention of integrated circuits in 1949} [that] made {the smartphones [that we use today]} possible.

“It” is the preparatory or dummy “it”

The first “that” is a pronoun with the referent “it” and "it" has the referent “the invention of integrated circuits”

The sentence can be restated as either

The invention of integrated circuits was in 1949. That invention of integrated circuits made possible the smartphones that we use today.

Or

The invention of integrated circuits [in 1949] made {the smartphones [that we use today]} possible.