For the record, I personally reserve judgement on old v. young earth as my faith and theology doesn’t turn on it. Each day could be a literal day, 1,000 years or each day could be an “age”.
As to young earth and science - there actually is a fair amount of sciene behind it and many books written to support it. Its a combination of the flood affecting our understanding of the fossel record - changes in atmoshphere, etc affecting carbon dating - and then believing that God created the universe with the appearance of age.
Its a lot to overcome in the face of what modern science tells us - but modern science is only a few hundred years old and could be wrong.
The key (IMO) is the belief/faith in the accurracy of the genesis story - that God is the creator and created man in His imagine and in the order described in the Genesis account.
We’ll find out in heaven, and our salvation wont turn on whether we are right or wrong on young earth or old earth.