Just set the limit stop on the RD. You will need to measure the exact roll out distance for the tyres you are using and at the pressures. All closed circuits will have these recorded with markings, and bikes do get checked regularly.
Junior cassettes are expensive because there is low demand. The 50 makes it a little more complicated, as the original numbers were set for standard 52 chainsets.
BTW:
52/16 = 3.25
34/11 = 3.09
Not a huge amount in it. If you have a smaller block, you can lock the front derailleur and run 11-25 or even 11-23. It is his first event, after all.
https://www.britishcycling.org.uk/zuvvi/media/bc_files/officials/Youth_Gear_Restrictions_-_Riders__Parents.pdf
BRITISH CYCLING GEAR LIMITS
CATEGORY GEAR LIMIT EXAMPLE FOR 700c WHEELS and a 23mm tyre.
Age category for the year. Roll out metres Approx Gear Inches Chain ring/Sprocket combinations that work.
Youth E Under 8 at 1st Jan 5.10 metres 64 inch 39×16 / 41×17 / 43×18 / 48×19
Youth D Under 10 at 1st Jan 5.40 metres 68 inch 41×16 / 43×17 / 46×18 / 49×19
Youth C Under 12 at 1st Jan 6.05 metres 76 inch 39×14 / 42×15 / 45×16 / 48×17
Youth B Under 14 at 1st Jan 6.45 metres 80 inch 39×13 / 42×14 / 45×15 / 51×17
Youth A Under 16 at 1st Jan 6.93 metres 88 inch 39×12 / 42×13 / 47×15 / 52×16
Junior Under 18 at 1st Jan 7.93 metres 100 inch 52×14