So then by definition 'modern science' excludes even the possibility of God having a hand in our origins.
Come up with a testable hypothesis regarding God's existence, and prove it to be true, and we'd HAVE to acknowledge God's role in our origins.
Not at all. Science just doesn't deal with things like "spirit" and things outside of nature (the super-natural) because they can't be observed, measured, or tested. Science deals only with those things with which it's methods are capable of dealing. The spirit world isn't accessable to the techniques of science.