Check your next shipment. The little piece of paper that is sometimes included in the box is a packing slip and is not suitable for customs purposes. Amazon is phasing these out as well for single box shipments they say to reduce waste. Amazon hasn't included invoices for items purchased in the US for delivery in the US for as long as I've had US account.
Both EPS and CPS send out frequent reminds to customers reminding them that they *must* submit an invoice for a shipment or that shipment may be delayed until the paperwork is received. Since all packages are opened stateside to verify contents, if an invoice was included, it would be removed and attached to the paperwork for the shipment and you'd never see it, thus you wouldn't know if it was there in the first place. Packing slips being of no interest to the courier or customs, if one is in the box, it usually stays in the box.
I'm prepared to admit that, I suppose, it's possible that some people's packages include an invoice, all I can say for certain that I have never received one and if I don't download and submit one myself, I get a nasty email telling me to do so forthwith.
What forwarder are you using that isn't asking you to supply an invoice?