Unfortunately, that’s not how induction works. To induce a statement, you show that if a statement holds for some value k then it also holds for value k+1 and you show that the statement holds for some minimum value k0. Thus established, the statement necessarily holds for all values not less than k0.

However, establishing that a pattern has some preceding element does not imply that the preceding element exists. In the language of induction, you’re trying to show that because the statement holds for all values greater than k0, it must hold for value k0.

As an illustrative example, an inductive statement could be that one cell will always divide into two cells after one hour, and a cell exists, therefore after 4 hours there will be 16 cells.

However, you cannot extend this pattern backward arbitrarily. In other words, you cannot say that because there are 16 cells, there must at one point have been half a cell from which the first whole cell originated. I believe that is the form of argument you’re trying to make here: the pattern holds starting at 1, and if the pattern held starting at 0 then 0 would lead to the pattern holding at 1; therefore the pattern must hold at 0. However, the logic doesn’t really work out that way.