What would be an ideal age to introduce musical instruments to children without being pushy.

Does it vary between genders? And what would be the best to introduce 1st?

Thank you

As soon as possible. There is no wrong age.

Children are interested in sounds. Some children are interested in how those sounds are made and how they affect other people. Not all of them are.

It’s best if the parent plays the instruments as sort of a "modeling" behavior. But pushiness is not necessarily a bad thing. Children need guidance and discipline/boundaries — they need to know what the rules are because learning an instrument does not provide immediate gratification.