Apart from the solutions that have already been mentioned, you can also:
Create your own "button" and assign a script to it:
- Go to Insert > Drawing and design your button

- Assign a script to it and type in the name of the function which ends up sorting your data

- You now have a button which sorts your data!
Create a custom menu using an onOpen trigger
You can make use of Apps Script's onOpen trigger in order to create a custom menu in your spreadsheet. This basically means that every time the spreadsheet is being opened, the new custom menu will get created and it will look something similar to this:

As for the code for this, it will end up following this structure more or less:
function onOpen(e) {
SpreadsheetApp.getUi()
.createMenu('Sorting Menu')
.addItem('Sorting A-Z', 'sortAZ')
.addToUi();
}
function sortAZ() {
//function to sort your data
}
Reference