I would top it up somehow. either more beer or glass marbled, stainless nuts, something to fill that headspace. the small barrels have so much more surface to volume than the big barrels already adding that much air to the headspace it going to introduce a lot of o2 which, unless you are very confident in the types of bugs you are adding could be bad news. unless you like RIS vinegar.
I don't think purgeing with co2 would do the trick, it might help but the barrel is not airtight so o2 is going to ingress no matter what.