Mikes solution works nicely, it can also be done by making an override for quantity-input.php.
The only problem is that after adjusting “input value”, the remaining “available” tickets calculations is wrong. If you have 10 tickets available and change default quantity to 1, the product will still state “10 available” and update only on quantity change.
Do anyone have a perspective on how to make the “available” count correctly with the changed default quantity?