Is it possible to combine or create conditional statements of 0 and 1, and optimize with an evolutionary algorithm (given that all computers use a binary system)?
Yes, evolutionary algorithms are very general, and can be used to modify almost any source data structure, including logic trees or even executable code, provided you have some measure of fitness to optimise for.
This can be taken to a highly abstract level, such as the paper Evolution of evolution: Self-constructing Evolutionary Turing Machine case study where an evolutionary algorithm is used to optimise other evolutionary algorithms which solve tasks using generic models of computing.
However, there are two important caveats:
There needs to be a measurement phase to establish the fitness of the algorithm. This can be very complex, depending on the problem you attempt to solve.
Genetic algorithms may be very general optimisers (capable of finding optimal solutions for problems when other algorithms may fail), but may also be very inefficient and slow depending on the size of the allowed genomes, and how the search space is structured relative to available genetic operations.
begin with the most fundamental operations (0 and 1, if then) to develop intelligence.
Provided the fitness measure allows for the expression of intelligence, then this seems theoretically possible - in the sense that there are no known reasons why a sufficiently complex logical machine could not be intelligent by any measure we have of abstract intelligence (excluding measures deliberately constructed to exclude computational models such as "intelligence is the capability of a living system . . .")
However, such a project faces some barriers which currently look insurmountable:
There is no formal measure of general intelligence to use as a fitness function. This could be worked around using an e-life approach of providing a suitable rich virtual environment and allowing agents to compete for resources in the hope that the most competitive agents would exhibit intelligent behaviour - but that begs the question of how you could recognise and select those agents through any objective measure.
Any environment rich enough to select for general intelligence, whilst simulating low-level agent logic is likely to require a lot of computation.
Our one example of evolving basic building blocks into beings we call intelligent took billions of years, whilst processing billions upon billions of separate evolving entities at any one time.
These last two points imply a computational cost far beyond current technology, so there is no route to actually running this experiment for real.