I would like to change the starting value of the number assigned to the
Invoice number on the Invoice template when clicking on the "Assign a Number"
button on the Invoice toolbar.

Does the "assign a number" button already exist? If yes, then hide
your starting number somewhere on your sheet- this will allow to Excel
to remember the number from use to use. Then have the code associated
with the button retrieve that number, augment it by one so the next
number is ready for use on the next invoice, and then add or apply the
number (now stored in memory) to your invoice number cell on the
template.