Reading Dedekind original manuscript (https://archive.org/details/essaysintheoryof00dedeuoft) it seems that he was after formalizing the completeness of the real numbers, which was known to him as the continuity of real numbers. Formalizing the completeness of real numbers then easily led him to construction of real numbers using cuts of rational numbers, which also provided a model for the real numbers(https://en.wikipedia.org/wiki/Dedekind_cut).
However, I have seen some sources talking about Eudoxus ratios (https://en.wikipedia.org/wiki/Eudoxus_of_Cnidus) being the predecessor of the Dedekind cuts, which sort of means that Dedekind knew how real numbers could be constructed using rational numbers. This in turn means that the Dedekind construction of real numbers suggested the completeness of real numbers to Dedekind.
So the question is that how did Dedekind conclude the real numbers are complete? Was he convinced that the reals were complete because they could be constructed using cuts of rational numbers (was this an acceptable (logical) argument to him)? or he followed a different logic?
In other words, what made Dedekind accept real numbers are complete, was it the construction of the real numbers or was it something else?