Then we don't exist, and neither does anything else.
Then there is no right or wrong; there just is. We are all just walking dirt powered by bioelectric impulses.
Then the oath has a minor technical error... of course, it can readily be argued that America is no longer a "republic" (run more as a democracy or an oligarchy), "indivisible" (see the basic fundamental philosophical differences between the Left half and the Right half of America), or has "Liberty and Justice for all" (thanks to affirmative action laws, income tax strata, "group rights", entitlements, etc.). Shall we delete these phrases as well?
"I pledge allegiance to the flag of the United States of America, and to the country for which it stands, one nation."
Kinda lacks zing, donchya think? ;^)
Back to your original question, "what if there is no [G]od?", I always clunk back against the concept of Origin... something started that Big Bang (or however the Universe began), and I choose to call Him (Her/It) "God"...
although I guess it could have been some mid-level arch-angel doing a really cool Heaven Science Fair project. j/k ;^)