D.M. Procida wrote:

The grout on the new shower is already showing signs of black mould
spores. Since we have a chance to nip this in the bud, what would be the
best way of doing so?

Commercial mould cleaner preparations are a mixture of bleach and sodium
hydroxide. If you want to replicate one dissolve two teaspoons of sodium
hydroxide in 500ml of water ensure that it is throughly dissolved then
add 100ml of bleach. Always add sodium hydroxide to water never the
other way around.

You can apply the solution using a spray bottle, and it's a good idea to
wear goggles when you do to avoid accidental splashback into the eye.

Leave to soak in for about 20 minutes then wash off. You can scrub it
into the grout using an old toothbrush.