If your son was charged with, and convicted of, criminal damage then he would probably be given either a conditional discharge or a referral order, which are explained here:
https://www.sentencingcouncil.org.uk/sentencing-and-the-council/types-of-sentence/types-of-sentences-for-young-people/
A conditional discharge becomes 'spent', under the provisions of the Rehabilitation of Offenders Act, immediately. A referral order becomes 'spent' as soon as the order comes to an end. (It can't last longer than a year).
However the matter might not even reach court, as it could be dealt with by the police directly, using either a youth caution (which becomes 'spent' immediately) or a youth conditional caution (which becomes 'spent' after three months.
Once a conviction (or caution) has become 'spent', it no longer appears on a check carried out through the Disclosure & Barring Service for most purposes. So, for example, if your son was to seek employment in an office or factory, with the employing requiring a DBS check before he commenced employment, his conviction/caution wouldn't show up. It would only show up on a check for certain 'sensitive' areas of employment (or, for example, voluntary work), such as those involving work with children, vulnerable adults or with the police or security services.
Even if a criminal conviction/caution does show up on such a 'sensitive area' check, it doesn't automatically mean that the person can't be taken on. So, for example, if your son applied to become a student teacher (or doctor, nurse, etc), his conviction/caution would show up but it's highly unlikely that a bit of stupidity at the age of 11 would have any bearing whatsoever upon his application.
Other than for courses leading to work with children, vulnerable adults or, say, the legal profession, universities don't carry out DBS checks on candidates anyway.
Other than when applying for positions in the 'sensitive' areas of employment or voluntary work mentioned above, anyone with 'spent' convictions or cautions can lawfully answer 'No' to a question which asks "Have you ever been convicted of a criminal offence?". That applies both to application forms for employment (or voluntary work) and to things like insurance forms.
So you've clearly been badly advised!