Can I find out when I bought my device

You can know it only from the invoice you have. The one which was given to you when you made the purchase. If it was from Apple Store you would have received the invoice on your email, provided by you to them while making the purchase. 

With online Order Status you can Print an Invoice

Hi,

Unfortunately, you can’t, you need to have with you the original receipt.

However, you can check the purchase date here.