Sending in an order and waiting for its arrival has aways been around and I think to try and see it as something different to a man with a van is impossible because the to were so intewrlinked and the link is available means of communication.
I have a book discussing clothing and making clothes at the beginning of the 19th century and the same women who were buying from local peddlers/ man in van equivalents were sending orders up to retailers in London, or sometimes just a local big town for lengths of cloth and other requisites. Later in the 19th - and early 20th century, big houses would write, or even telegraph orders to Harrods, and Army & Navy Stores and other department stores or big food purveyors, who would pack the food into hampers and it would be sent by train to the nearest station and collected. Not that different to ordering groceries online.
Until the 1970s, and for some after that, many homes could not afford telephones, so there was no alternative to a trader loading goods in his van/cart and taking them to his customers to choose what they wanted, or them writing off and ordering them or even using catalogues (mail order).
Supermarket deliveries evolved from the small local individual businesses, with their horse and cart or man in van, who the supermarkets put out of business and found that they neededto replace.