I have got two queries
1. If Imamat were to be part of belief (Usool e Deen) then why Allah
did not ask us explicitly to believe in Imamat as He has number of times asked us in Quran to believe in Allah, Rasool, Maad, Angles and the Books. We do not find Imamat any where in Quran mentioned alongwith the list of other Usool e Deen. We deduce it separately by
connecting bits and pieces from various ayats disregarding the context
and mostly rely on the Hadees to build the concept.

2. If Allah’s design was to have 12 successive Imams (from Aale
Rasool) after the last prophet to lead the Ummah then it means if
things had gone as per Allah’s initial design this world  would have
ended (Qiyamat) somewhere around 350 Hijra, maximum 100 years after the birth of Akhir uz Zamman, because its illogical to assume that
each Imam or the last one would have lived a life spreading over
thousands of years where other human beings and even the prophets
lived normal span of life, and if now this world is continuing to survive, its because we the humans because of our Irada o Ikhtiar did
not let the Imamat prevail.

1) Scholars divide the Usul al Din into 2 categories. There is one category that Islam relies upon, that is Towhid, Prophethood and belief in Judgement day. The other 2 beliefs (Adela, and Imamate) are Usul al Din of the Shia. It means a person with complete faith beliefs in those, however not believing in the latter two does not make someone not a Muslim.

However we have many hadith from the Imams of the Ahlulbayt that discuss the importance of the position of Imamate. The Imam is the one who guides to Allah.

Zurara narrates from Imam al Baqir that Islam was built upon 5
عَنْ زُرَارَةَ ، عَنْ الإمام محمد بن علي الباقر ( عليه السلام ) أنهُ قَالَ : " بُنِيَ الْإِسْلَامُ عَلَى خَمْسَةِ أَشْيَاءَ : عَلَى الصَّلَاةِ ، وَ الزَّكَاةِ ، وَ الْحَجِّ ، وَ الصَّوْمِ ، وَ الْوَلَايَةِ " .
قَالَ زُرَارَةُ فَقُلْتُ : وَ أَيُّ شَيْءٍ مِنْ ذَلِكَ أَفْضَلُ ؟
فَقَالَ : " الْوَلَايَةُ أَفْضَلُ ، لِأَنَّهَا مِفْتَاحُهُنَّ ، وَ الْوَالِي هُوَ الدَّلِيلُ عَلَيْهِنَّ

ما نودي بشيئ كما نودي بالولاية

The Imam says Islam was built upon 5, salaat, zakaat, hajj, sawm, and Wilaya. Then the Imam says the wilaya is the most important because the Imam guides people to all of the other acts of worship.

Furthermore the faith was complete on the day of Ghadeer after the appointment of Imam Ali.

2) We don’t really know that the world would have ended. Perhaps the Imams would have lived longer lives like Noah. Things happen for a reason, however the fact that life continues should not justify the disobedience of God.