I'm not sure how many people really think that everyone starts from the same place or doesn't understand that there are people with disadvantages.
Even most conservatives in western countries believe there needs to be a health care system, an education system, that works for all. There are different ideas about what works best, and it's really not at all clear that the best systems are the ones that are the most completely socialized and government run. But the reason most people think that is because they see those are areas that make a huge difference to what those with disadvantages can achieve.
Most conservatives however also think that if you create systems of dependence on it, it ultimately disempowers people and undermines important forms of community resilience. So there is a balance to be struck and it is not always simple. And then at another level, when people are dependent on an entity like the state, or equally a corporation, they are at the mercy of that organization in a way that is ultimately politically dangerous and also dehumanizing.
I watched an interesting film the other day about black conservatibes in the US, and I was really struck by the way many of them percieved the approach of the Democratic party. They felt that the DP was happy to give black Americans a certain amount of state support, so long as they remained in some kind of underclass position and dependent (apart from a few token examples) so they would continue to vote Democrat and not contest other types of Democratic policies. And they say this as a continuation of earlier DP policies like Jim Crowe laws, which also looked to use the black community to gain votes in another way.
Which is to say, they saw the actions of the left, the DP, as purposefully maintaining policies that damaged their ability to better themselves.
Now whether or not you think that analysis is correct, I think it gives some window into how people can think quite differently about what kind of social policy creates opportunities for people to thrive,