Just noticed that there seem to be no Greek words beginning with σλ-. Would that have been regarded as an unacceptable consonant cluster? If so, it seems odd in a language that has no objection to σκ-, σμ-, and others. And might it explain the α inserted in the biblical name Σαλωμὼν, where “Σλωμὼν” would be closer to the Hebrew?
The need for a vowel doesn’t necessarily explain the choice of the vowel.
My best guess as to why alpha was chosen is that it was the vowel in the word shalom “peace”, that it was derived from. That is to say that I think it was a deliberate return to the etymology of the word.
I don’t know Greek we’ll enough to be able to say that an alpha would have been the most natural or euphonic vocal sound to have naturally arisen in the mouth of a Greek speaker at the time and place it was borrowed.