So, why don't we start the Torah as soon as we get it ?

In other words, why do we start and end the Torah on Simchas Torah - when we actually received it on Shavuos ? Wouldn't that be a more appropriate time ?

I was asked this question by a very chashuve Jew.

The Gemara in Megilla ( 31b) states : "Ezra established for all of Israel that they should read the warnings in sefer Vayikra before Shavuos and the warnings in sefer Devarim before Rosh Hashanna. Why ? So that the year and it's misfortunes should exit together."
In other words, the cycle of Torah readings reflects the time of year that we find ourselves in. This cycle was generated in order to get the most meaningful associations and lessons from the parshiyos.
One question still remains, however, since when is Shavuos the same as Rosh Hashanna ?!
The gemara answers that on Shavuos we are judged regarding tree fruits - so it's like Rosh Hashanna which is also a day of judgment.
Another answer that occured to me was that Shavuos and Rosh Hashanna really do share a common purpose - they both commemorate the creation of the world.
You see, when the Torah recounts the days of creation it mentions the sixth day as the "yom HAshishi" ("THE Sixth day" - these are also the words we start kiddush with.) The gemara [Shabbos 88a] states that this refers, not to the sixth day of creation, but is in fact alluding to the sixth of Sivan, Shavuos.
The world was created on condition that the Jews give it purpose - which they did by receiving the Torah. So, Shavuos is a commemoration of creation ( or at least the reason for it ) and Rosh Hashanna is the day of creation - and since they both represent renewals we aim to finish up those scary parshiyos of tochacha before hand - so we can start on a positive note.

Let's gear up for a day of renewal in our service of Hashem and devotion to His Torah - more importantly - realize the whole world is counting on you !
- Hatzlacha !