The infamous laryngeal theory states that Sanskrit a originates from PIE h2e. Furthermore, the unconditional change of e/o to a is what the linguists call a merger. But both are faulty statements, shown almost no rejection simply because few appear able to speak up against it. The theory demonstrates just how little Hermann Möller and Ferdinand De Saussure actually knew about so called laryngeals or semetic languages. Hermann Möller, noted for having compared both Semetic and Indo-European languages, was apparently oblivious to the fact that the pharyngeal consonants of Arabic and Hebrew, tend to advance an a vowel to æ. This is very surprising indeed. It may be that he was so blinded by Eurocentrism, that he failed to see how dubious his assumptions really were.
The a coloring laryngeal, as it is called, is said to have colored PIE e to a in Sanskrit, but from what we know the opposite would've occurred. And what better way to prove that then to go to Arabic, a language infested with laryngeal consonants. In Arabic, a is advanced to æ in the environment of most consonants:
- (/m/, /b/ and /f/),
- plain (non-emphatic) with the exception of /r/ (/θ/, /ð/, /n/, /t/, /d/, /s/, /z/, /l/, /ʃ/ and /d͡ʒ~ɡ~ʒ/)
- (/ħ/ and /ʕ/)
- (/h/ and /ʔ/)
- /j/, /k/ and /w/;
- Across and West Asia, the allophones [æ] and [ɑ] may be realized differently, either as [a ~ ɑ ~ ɛ], or both as [a ~ ä]
- In northwestern Africa, the open front vowel /æ/ is raised to ɛ or e.
But lets not stop at Arabic. It is well known that Proto Semitic ā became ō in Ancient Hebrew, for reasons not fully understood. Changes like this also occurred in the Great Vowel Shift of the English language istself, where long a become eɪ. The opposite shift however, was not observed.
In Romani words derived from Sanskrit, the change was common. See this link for more information.
I conclude from these facts that the Sanskrit vowel a is the original, which shifted to æ, then to e in European dialects like Hellenic and Italic. In some places it shifted to o, this shift being less common than the former one. This reconstruction is typologically stable, given that a plain unrounded open vowel is the most common sound in the world. Such dubious claims of PIE having had only /e/ are to be regarded warily. Abkhaz has only two distinct vowels (a/ə) , not e, a fact that has so far been altogether ignored.
Though some will look the Hittite for objections, the fact remains that Hittite ḫ and ḫḫ almost never occur initially, something that should be expected of any laryngeal, and are normally followed by an a, not e. These sounds would have been e and o coloring laryngeals if pharyngeal, as these consonants tend to draw following a towards æ, and if labial, towards o. Let us not forget that the glottal consonants h and aleph also advance a to ae in Arabic.
Thus, there was no e or o grade in PIE, and how these grades developed in western dialects can be easily explained like this. In Stage I, during the breakup of PIE, the accusative m influenced the preceding a vowel, and having an labial articulation, caused a fairly straightforward shift of a > o. So then we are left with a nominative -as, a vocative -a, and the accusative -om. It is obvious that this leaves a slightly awkward paradigm. So in Stage II, an o grade was created for all words wherein had the case ending -om. It would be wrong to say that the original a grade was entirely replace. No, it survived in many words. After all, who said sound change was uniform. I do believe that the emergence of the grade might've been motivated by a sort of trend.
As for the e grade, dental consonants influenced a and caused the shift of a > e, like the s in -as for example, resulting in this grade.
From this data, I reconstruct these endings for the PIE masculine singular A stem.
Note: The ergative case is doubtful, reconstructed only on the basis of Hittite and certain ergative features in Vedic and Greek. Furthermore, the neuter a stem had the ending -at for its instrumental case.
Here are some enlightening articles that deal with the subject.  After reading them an weighing the evidence for or against the presence of laryngeals in PIE, I was lead to the following conclusion.
Semitic and Uralic evidence does prove that, at some stage, PIE either had pharyngeal consonants, or a plain glottal stop. But the Hittite phoneme transcribed as ḫ, ought not to be considered a reflex of these consonants. The reason being that it is the glottal stop that causes vowel lengthening (Iraqi dialect of Arabic for example), not pharyngeal consonants. And since ḫ is a velar fricative in Sumerian, and an uvular fricative in Akkadian, it could not have possibly been a glottal stop in Hittite. Neither, if it was a velar fricative, would it have a single chance of leaving a long vowel in its wake. Hittite was probably influenced by the surrounding languages that had these sounds, and there are plenty of them. Sumerian to the south, Egyptian to the west, Akkadian to the east, and Caucasian languages to the north.
This demonstrates that the Anatolian branch drifted off earlier from the Urheimat than the rest. Over time it lost its original character: merging the masculine and feminine genders, borrowing two sounds, and simplifying the originally complex verb conjugations. How can it be said that Hittite was more preservative than Indo-Aryan, just because it was supposedly written down earlier. Shikaripura Ranganatha Rao has already deciphered the Indus Script, written from 3500–1900 BCE, and revealed it to be Sanskrit. This pushes Sanskrit's age back by over two millennia, which means that the tongue of the Vedas and PIE weren't much different from each other after all.