Matcha powder can be found on Amazon, I would recommend using the Ito-en brand. If not using this brand, make sure the product is made in Japan and the ingredients to ensure nothing else is mixed in!
The trick to making this quickly is keeping the cream cool. Traditional ice cream recipes have you heat both cream and milk in the pot. By keeping out the cream, you help to quickly cool the hot milk when you add it to your bowl for chilling. You could even stick the cream in the freezer for a bit. Just make sure you don’t freeze it!