Let me begin (pun intended) by explaining that we do not read the entire “portion of the week” called Genesis on Simchat Torah. We read only the very beginning of the portion of Genesis on Simchat Torah. Then we read the entire portion of Genesis on Shabbat. Of course we re-read the first part of the weekly portion on Shabbat since it is part of the entire Torah portion for this week.
You might ask, “Why then do we even bother to read the first part of the portion of Genesis on Simchat Torah if anyway we are going to re-read it and complete the reading of the entire portion on the coming Shabbat?
The reason is that since we read the last portion of the Torah on Simchat Torah – as you write – we also want to show that the Torah "never ends". There is no true “in the beginning” and “in the end” when it comes to the Torah. The Torah is timeless and infinite and helps us to connect to the Creator of the Heavens and the Earth and Mankind. We should never feel that we have ever really finished reading and learning the Torah. Therefore, we start right away on Simchat Torah to read a small amount from the beginning of Genesis to show that we are never really finished.