Yes, you can start the numbering of your invoices and quotes wherever you want. For that, you have to change the numbers manually by clicking on Actions > Edit invoice/quote details when you're in a quote or invoice. You can define any pattern you want (adding the year, for example) and the system will try to increment this number for the next documents.
Please note that the system will do its best to increment the numbers correctly. If you define 2017-0035, it will of course name the next quote 2017-0036. But if you defined 0035-2017, for example, it may increment it to 0035-2018, so make sure the number to be incremented it at the end.
Also, if you change a number to add the name of the client in it (e.g. Microsoft - 2017-0035), please note that the system will keep the name of this client in the next quotes you create, even if they concern other clients (because it only increments the number).