Imagine a gang of thieves that was planning to rob a bank in the dead of night as they were aware that it had recently received delivery of some gold bullion.
Another gang, smaller and less powerful, finds out about their plans and seeks to pre-empt them by reaching the bank earlier in order to raid it first.
Whoever steals the gold first will keep it, right?
When the first gang finds out, they rush to the bank to find their rivals about to make their plunder.
They attempt to stop them. The second gang, seeing that they are going to lose to this stronger gang, offer to divide the goods 50-50.
The first gang does not agree to the deal and wants everything for itself.
There is a gunshot and one of their rival gang members is killed.
The powerful gang triumphs and walks away with their loot.
Here is the question: would you expect, in that moment, for either of the gangs to be discussing who the gold bullion actually and rightfully belonged to?
I leave you with the narrative on what transpired at Saqifa Bani Sa'ida from Sahih al-Bukhari in the words of one of the participants, ‘Umar b. al-Khattab, who famously explained how Abu Bakr came to power when he feared that people were planning to give allegiance to ‘Ali after him:
(O people!) I have been informed that a speaker amongst you says, 'By Allah, if `Umar should die, I will give the pledge of allegiance to such-and-such person.'
One should not deceive oneself by saying that the pledge of allegiance given to Abu Bakr was given suddenly and it was successful. No doubt, it was like that, but Allah saved (the people) from its evil, and there is none among you who has the qualities of Abu Bakr.
Remember that whoever gives the pledge of allegiance to anybody among you without consulting the other Muslims, neither that person, nor the person to whom the pledge of allegiance was given, are to be supported, lest they both should be killed.
And no doubt after the death of the Prophet (ﷺ) we were informed that the Ansar disagreed with us and gathered in the shed of Bani Sa`da.
`Ali and Zubair and whoever was with them, opposed us, while the emigrants gathered with Abu Bakr.
I said to Abu Bakr, 'Let's go to these Ansari brothers of ours.' So we set out seeking them, and when we approached them, two pious men of theirs met us and informed us of the final decision of the Ansar, and said, 'O group of Muhajirin (emigrants) ! Where are you going?' We replied, 'We are going to these Ansari brothers of ours.'
They said to us, 'You shouldn't go near them. Carry out whatever we have already decided.'
I said, 'By Allah, we will go to them.' And so we proceeded until we reached them at the shed of Bani Sa`da. Behold! There was a man sitting amongst them and wrapped in something. I asked, 'Who is that man?' They said, 'He is Sa`d bin 'Ubada.' I asked, 'What is wrong with him?' They said, 'He is sick.'
After we sat for a while, the Ansar's speaker said, 'None has the right to be worshipped but Allah,' and praising Allah as He deserved, he added, 'To proceed, we are Allah's Ansar (helpers) and the majority of the Muslim army, while you, the emigrants, are a small group and some people among you came with the intention of preventing us from practicing this matter (of caliphate) and depriving us of it.'
When the speaker had finished, I intended to speak as I had prepared a speech which I liked and which I wanted to deliver in the presence of Abu Bakr, and I used to avoid provoking him. So, when I wanted to speak, Abu Bakr said, 'Wait a while.' I disliked to make him angry.
So Abu Bakr himself gave a speech, and he was wiser and more patient than I. By Allah, he never missed a sentence that I liked in my own prepared speech, but he said the like of it or better than it spontaneously.
After a pause he said, 'O Ansar! You deserve all (the qualities that you have attributed to yourselves, but this question (of Caliphate) is only for the Quraish as they are the best of the Arabs as regards descent and home, and I am pleased to suggest that you choose either of these two men, so take the oath of allegiance to either of them as you wish.
And then Abu Bakr held my hand and Abu Ubaida bin al-Jarrah's hand who was sitting amongst us. I hated nothing of what he had said except that proposal, for by Allah, I would rather have my neck chopped off as expiator for a sin than become the ruler of a nation, one of whose members is Abu Bakr, unless at the time of my death my own-self suggests something I don't feel at present.'
And then one of the Ansar said, 'I am the pillar on which the camel with a skin disease (eczema) rubs itself to satisfy the itching (i.e., I am a noble), and I am as a high class palm tree! O Quraish. There should be one ruler from us and one from you.' Then there was a hue and cry among the gathering and their voices rose so that I was afraid there might be great disagreement, so I said, 'O Abu Bakr! Hold your hand out.' He held his hand out and I pledged allegiance to him, and then all the emigrants gave the Pledge of allegiance and so did the Ansar afterwards.
And so we became victorious over Sa`d bin Ubada (whom Al-Ansar wanted to make a ruler).
One of the Ansar said, 'You have killed Sa`d bin Ubada.' I replied, 'Allah has killed Sa`d bin Ubada.'
`Umar added, "By Allah, apart from the great tragedy that had happened to us (i.e. the death of the Prophet), there was no greater problem than the allegiance pledged to Abu Bakr because we were afraid that if we left the people, they might give the Pledge of allegiance after us to one of their men, in which case we would have given them our consent for something against our real wish, or would have opposed them and caused great trouble. So if any person gives the Pledge of allegiance to somebody (to become a Caliph) without consulting the other Muslims, then the one he has selected should not be granted allegiance, lest both of them should be killed."
Source - Sahih al-Bukhari - Sayings and Teachings of Prophet Muhammad (صلى الله عليه و سلم)