The Earth and the Universe are measured by scientists (not very accurately) to be billions of years old. While their estimates vary across billlions of years I am not too bothered by such blunt results and am happy to accept the age they appear to be as roughly accurate.
So your camp would immediately reply with something like - 'so then the Bible in Genesis and the entire OT chronology must be wrong so God could not have inspired it because He doesn't make mistakes according to your understanding'.
It's an understandable leap but also a leap into the dark, you see Adam was created a mature man, Eve a mature women, in other words they were along the usual life cycle when they appeared on Earth. Technically you could have met Adam (using a time machine!) and ask him how old he was, and he could have told you (while looking around 30) that he was three days old.
In a similar way you could have walked into the wedding in
John 2, in Cana in Galilee. You would drink the wine and estimate it to be maybe 5-10 years of age, yet it was only minutes old because Christ turned water into that wine five minutes before you arrived.
So you see the Universe may have the appearance of a very old age, but in fact it doesn't actually need to be any older or younger than the Bible says it is.