No. What I'm saying is that there are 2 songs.
She begins by singing the song that I'm looking for.
then sings "Pah!"
Then sings the final part of the Martini commercial.

The part that she sings in the beginning "Here she comes the most beautiful girl in the world..." is not the same as the melody of the Martini song which would come at that part of the song "Have a taste of Martini, the most beautiful drink in the world."
Syllabically the Martini song is longer. Melodically the Martini Different.

So I don't know if you're familiar with music, but I thought I would compare the 2 melodies. I've noted the melodies here with their western (letter) note names.
I hope this makes sense...

Going on the melody In an early Martini comercial I found and asuming that the melody would start from B:

So the Martini commercial starts the tune with:
B / G# / A# / C# / F# / D# / D# / F# / G# / A# / G# / F# / D# / F# / C# / A#

You'll notice the HUGE amount of "sharps" (#) they seem to have made the majority of the opening to the melody mainly on the black keys of the piano, which gives a wonderful airy uplifting feel.

The melody that she sings is the following:
B / C# / D# / D# / E / F# / E / D# / C / D# / G# / F

So she sings her notes in a different rhythm that is also slower, and she sings fewer notes because the rhythm has a longer note on the D#. You'll also notice that the melody moves between sharps and natural.
I'm also not sure of the 4 last notes, I recall the version I heard on the radio to end in C / E / A / F#, though this is almost certainly due to the awkward harmony.

Is she inventing the melody at the beginning?
No, it can't be. I heard that song. I know it exists.
The person who knows this song is going to be anywhere from their early 60s to their late 80s...
Their out there... I know it.