Back in the 1950s musicals played a much larger part in popular culture. When My Fair Lady finally opened in New York and the original cast album was released (in monophonic only, as stereo was only beginning to gain traction; a stereo recording was made and released a year or so later), it was the highest selling record of 1956.

So the Philadelphia Inquirer published several articles about the show and its stars during its run, as well as reviewing it when it finally opened.

That review by Henry Murdock begins:

While trying to marshal our thoughts after a beautiful evening and channel them into a semi-coherent recital of the many glories of “My Fair Lady,” let us state quickly that this is one of the top musicals.
It will take its place in memory we are sure, with such shows as “Show Boat,” “Oklahoma!”, “Carousel,” “Finian’s Rainbow, “Brigadoon,” and all the other rarities which live and breathe and give pleasure 10 or 20 years after their initial bow.

And it goes on in that vein.

There is recognition that Julie Andrews was on her way to stardom.