Did the solar system start out with a uniform distribution of elements or was the distribution uneven?
The Sun was born with abundances that reflect those of the initial gas cloud it formed from. These abundances have since been modified by interior nuclear processes. The rest of the objects in the Solar System have abundance mixtures that are informed by a variety of chemical differentiation processes and in general don't reflect the initial abundances of the protostellar gas cloud. The exception are meteorites, which apart from having little hydrogen, helium or noble gases are otherwise though to be quite representative.
The chemical elements that the Sun formed with are thought to be representative of the gas cloud from which the Sun and Solar System formed.
Those elemental abundances have since been modified by nuclear reactions within the Sun. For example, most (99%) of the initial Li has been burned; the initial deuterium has all gone; some of the initial hydrogen (about 40% of the core hydrogen, which is a bit less than 10% of the total hydrogen the Sun was born with) has been transformed into helium; there have been much smaller changes in the abundances in carbon, nitrogen (increased) and oxygen as a result of the CNO cycle which operates at a low level in the Sun. Note that working out the true average abundances in the Sun is complicated by the fact that there is some chemical differentiation and diffusion that will take place over billions of years (e.g., Asplund et al. 2021).
The raw material for the rest of the Solar System was the same, but it was drastically affected by processes that occured before and during the formation of planetary and other solid bodies.
For example, there is a tendency for solids to form close to the mid plane of the circumsolar disk that forms around the Sun; only solids with low volatility can form close to the Sun and these tend to be rich in heavier elements; more abundant ices, rich in hydrogen can form further out. Much of the hydrogen and helium in the initial gas cloud was not incorporated into solids and is lost when gas is expelled from the early Solar System, though some fraction of it was accreted onto the gas giants. The gas giants Jupiter and Saturn are the closest in terms of the overall abundance mixture to the composition of the Sun and the protosolar gas cloud.
Meteorites are an interesting exception. These were formed very early in the protosolar environment. Aside from having very little hydrogen, helium, noble gases and being somehwat depleted in carbon, nitrogen and oxygen, the abundance mixture of everything else (often expressed as a ratio to silicon) is probably very similar to the protosolar gas cloud and indeed to the present day Sun, aside from the elements discussed above (e.g., Lodders 2003).