Besides for the obvious answer, that Shabbos is the most convenient time, the Madanay Asher suggests another answer based on a Chasam Sofer:
The Chasam Sofer (Kedoshim) says something incredible on the pasuk: איש אמו ואביו תרא ו ואת שבתותי תשמרו – “A man shall fear his mother and father, and he shall guard Shabbos” What is the connection between fearing parents and keeping Shabbos? The Chasam Sofer explains: One could ask, why should one respect his parents, they have done something terrible by bringing him into the world. The Gemara in Eruvin (13b) tells us: נח לו לאדם שלא נברא משנברא – “It would have been better for a person not to have been created”. The Gemara explains: It is better for man not to have been created as there are so many aveiras and it is very easy to sin, and one is more likely to get punished then rewarded. However, the Gemara in Shabbos (118b) teaches: “Anyone who keeps Shabbos properly, has his sins atoned for”. Therefore, on Shabbos it is worth being created. With this the Chasam Sofer explains the above pasuk: One must respect his parents, and if you will ask why? Surely, they did something wrong by bringing him into the world? The pasuk answers: There is a mitzvah of Shabbos, and if one keeps it his sins are atoned, therefore, it is good that he was brought into the world.
Based on this, we can understand why we wait until Shabbos to make a kiddush. During the week one has is not very happy that he was created, however, on Shabbos the simcha is complete as if one keeps Shabbos his sins are atoned for. Because of Shabbos it is worth being created, therefore, we wait until Shabbos to make a kiddush.
